acl2-books-certs 6.3-5 / usr / share / acl2-6.3 / books / cutil / defprojection-tests.cert

(IN-PACKAGE "ACL2")
"ACL2 Version 6.3"
:BEGIN-PORTCULLIS-CMDS
(INCLUDE-BOOK "portcullis")
:END-PORTCULLIS-CMDS
:EXPANSION-ALIST
((3 RECORD-EXPANSION (MAKE-EVENT (PROG2$ (CW "~%~%~%WARNING!  PRINTER ON FIRE!~%You are loading ~
       cutil/defprojection-tests! Don't do that!~%~%") (QUOTE (VALUE-TRIPLE :INVISIBLE))) :CHECK-EXPANSION T) (MAKE-EVENT (PROG2$ (CW "~%~%~%WARNING!  PRINTER ON FIRE!~%You are loading ~
       cutil/defprojection-tests! Don't do that!~%~%") (QUOTE (VALUE-TRIPLE :INVISIBLE))) :CHECK-EXPANSION (VALUE-TRIPLE :INVISIBLE))) (6 RECORD-EXPANSION (CUTIL::DEFPROJECTION CUTIL::DUPE-LIST (CUTIL::X) (CUTIL::DUPE CUTIL::X) :OPTIMIZE NIL) (WITH-OUTPUT :STACK :PUSH :OFF :ALL :ON ERROR (PROGN (TABLE INTRO-TABLE :MARK (QUOTE CUTIL::DUPE-LIST)) (RECORD-EXPANSION (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (LOGIC) (DEFUND CUTIL::DUPE-LIST-EXEC (CUTIL::X CUTIL::ACC) (DECLARE (XARGS :GUARD T :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (IF (CONSP CUTIL::X) (CUTIL::DUPE-LIST-EXEC (CDR CUTIL::X) (CONS (CUTIL::DUPE (CAR CUTIL::X)) CUTIL::ACC)) CUTIL::ACC)) (DEFUND CUTIL::DUPE-LIST (CUTIL::X) (DECLARE (XARGS :GUARD T :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (MBE :LOGIC (IF (CONSP CUTIL::X) (CONS (CUTIL::DUPE (CAR CUTIL::X)) (CUTIL::DUPE-LIST (CDR CUTIL::X))) NIL) :EXEC (REVERSE (CUTIL::DUPE-LIST-EXEC CUTIL::X NIL)))) (SET-INHIBIT-WARNINGS "disable") (LOCAL (MAKE-EVENT (IF (CUTIL::IS-THEOREM-P (QUOTE CUTIL::DUPE-LIST-NIL-PRESERVINGP-LEMMA) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (DEFTHM CUTIL::DUPE-LIST-NIL-PRESERVINGP-LEMMA (OR (EQUAL (ALISTP CUTIL::X) T) (EQUAL (ALISTP CUTIL::X) NIL)) :RULE-CLASSES :TYPE-PRESCRIPTION :HINTS (("Goal" :IN-THEORY (QUOTE ((:TYPE-PRESCRIPTION ALISTP))))))))))) (DEFTHM CUTIL::DUPE-LIST-WHEN-NOT-CONSP (IMPLIES (NOT (CONSP CUTIL::X)) (EQUAL (CUTIL::DUPE-LIST CUTIL::X) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST-OF-CONS (EQUAL (CUTIL::DUPE-LIST (CONS CUTIL::A CUTIL::X)) (CONS (CUTIL::DUPE CUTIL::A) (CUTIL::DUPE-LIST CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::TRUE-LISTP-OF-DUPE-LIST (EQUAL (TRUE-LISTP (CUTIL::DUPE-LIST CUTIL::X)) T) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST-WHEN-NOT-CONSP CUTIL::DUPE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::LEN-OF-DUPE-LIST (EQUAL (LEN (CUTIL::DUPE-LIST CUTIL::X)) (LEN CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST-WHEN-NOT-CONSP CUTIL::DUPE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CONSP-OF-DUPE-LIST (EQUAL (CONSP (CUTIL::DUPE-LIST CUTIL::X)) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST-WHEN-NOT-CONSP CUTIL::DUPE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CAR-OF-DUPE-LIST (EQUAL (CAR (CUTIL::DUPE-LIST CUTIL::X)) (IF (CONSP CUTIL::X) (CUTIL::DUPE (CAR CUTIL::X)) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST-WHEN-NOT-CONSP CUTIL::DUPE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CDR-OF-DUPE-LIST (EQUAL (CDR (CUTIL::DUPE-LIST CUTIL::X)) (CUTIL::DUPE-LIST (CDR CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST-WHEN-NOT-CONSP CUTIL::DUPE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST-UNDER-IFF (IFF (CUTIL::DUPE-LIST CUTIL::X) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST-WHEN-NOT-CONSP CUTIL::DUPE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST-OF-LIST-FIX (EQUAL (CUTIL::DUPE-LIST (LIST-FIX CUTIL::X)) (CUTIL::DUPE-LIST CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST-WHEN-NOT-CONSP CUTIL::DUPE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST-OF-APPEND (EQUAL (CUTIL::DUPE-LIST (APPEND CUTIL::X CUTIL::Y)) (APPEND (CUTIL::DUPE-LIST CUTIL::X) (CUTIL::DUPE-LIST CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST-WHEN-NOT-CONSP CUTIL::DUPE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST-OF-REV (EQUAL (CUTIL::DUPE-LIST (REV CUTIL::X)) (REV (CUTIL::DUPE-LIST CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST-OF-APPEND CUTIL::DUPE-LIST-WHEN-NOT-CONSP CUTIL::DUPE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST-OF-REVAPPEND (EQUAL (CUTIL::DUPE-LIST (REVAPPEND CUTIL::X CUTIL::Y)) (REVAPPEND (CUTIL::DUPE-LIST CUTIL::X) (CUTIL::DUPE-LIST CUTIL::Y))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST-OF-APPEND CUTIL::DUPE-LIST-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::NTHCDR-OF-DUPE-LIST (EQUAL (NTHCDR CUTIL::N (CUTIL::DUPE-LIST CUTIL::X)) (CUTIL::DUPE-LIST (NTHCDR CUTIL::N CUTIL::X))) :HINTS (("Goal" :INDUCT (NTHCDR CUTIL::N CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (NTHCDR CUTIL::DUPE-LIST-WHEN-NOT-CONSP CUTIL::DUPE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MEMBER-EQUAL-OF-DUPE-IN-DUPE-LIST-WHEN-MEMBER-EQUAL (IMPLIES (MEMBER-EQUAL CUTIL::A (DOUBLE-REWRITE CUTIL::X)) (MEMBER-EQUAL (CUTIL::DUPE CUTIL::A) (CUTIL::DUPE-LIST CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (MEMBER-EQUAL CUTIL::DUPE-LIST-WHEN-NOT-CONSP CUTIL::DUPE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SUBSETP-EQUAL-OF-DUPE-LISTS-WHEN-SUBSETP-EQUAL (IMPLIES (SUBSETP-EQUAL (DOUBLE-REWRITE CUTIL::X) (DOUBLE-REWRITE CUTIL::Y)) (SUBSETP-EQUAL (CUTIL::DUPE-LIST CUTIL::X) (CUTIL::DUPE-LIST CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (SUBSETP-EQUAL CUTIL::MEMBER-EQUAL-OF-DUPE-IN-DUPE-LIST-WHEN-MEMBER-EQUAL CUTIL::DUPE-LIST-WHEN-NOT-CONSP CUTIL::DUPE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST-EXEC-REMOVAL (EQUAL (CUTIL::DUPE-LIST-EXEC CUTIL::X CUTIL::ACC) (REVAPPEND (CUTIL::DUPE-LIST CUTIL::X) CUTIL::ACC)) :HINTS (("Goal" :INDUCT (CUTIL::DUPE-LIST-EXEC CUTIL::X CUTIL::ACC) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST-EXEC CUTIL::DUPE-LIST-WHEN-NOT-CONSP CUTIL::DUPE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (VERIFY-GUARDS CUTIL::DUPE-LIST-EXEC :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST-EXEC)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (VERIFY-GUARDS CUTIL::DUPE-LIST :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST CUTIL::DUPE-LIST-EXEC-REMOVAL CUTIL::TRUE-LISTP-OF-DUPE-LIST REVERSE-REMOVAL REVAPPEND-REMOVAL REV-OF-APPEND REV-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (LOCAL (IN-THEORY (ENABLE CUTIL::DUPE-LIST CUTIL::DUPE-LIST-WHEN-NOT-CONSP CUTIL::DUPE-LIST-OF-CONS))))) (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (LOGIC) (DEFUND CUTIL::DUPE-LIST-EXEC (CUTIL::X CUTIL::ACC) (DECLARE (XARGS :GUARD T :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (IF (CONSP CUTIL::X) (CUTIL::DUPE-LIST-EXEC (CDR CUTIL::X) (CONS (CUTIL::DUPE (CAR CUTIL::X)) CUTIL::ACC)) CUTIL::ACC)) (DEFUND CUTIL::DUPE-LIST (CUTIL::X) (DECLARE (XARGS :GUARD T :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (MBE :LOGIC (IF (CONSP CUTIL::X) (CONS (CUTIL::DUPE (CAR CUTIL::X)) (CUTIL::DUPE-LIST (CDR CUTIL::X))) NIL) :EXEC (REVERSE (CUTIL::DUPE-LIST-EXEC CUTIL::X NIL)))) (SET-INHIBIT-WARNINGS "disable") (RECORD-EXPANSION (LOCAL (MAKE-EVENT (IF (CUTIL::IS-THEOREM-P (QUOTE CUTIL::DUPE-LIST-NIL-PRESERVINGP-LEMMA) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (DEFTHM CUTIL::DUPE-LIST-NIL-PRESERVINGP-LEMMA (OR (EQUAL (ALISTP CUTIL::X) T) (EQUAL (ALISTP CUTIL::X) NIL)) :RULE-CLASSES :TYPE-PRESCRIPTION :HINTS (("Goal" :IN-THEORY (QUOTE ((:TYPE-PRESCRIPTION ALISTP))))))))))) (LOCAL (VALUE-TRIPLE :ELIDED))) (DEFTHM CUTIL::DUPE-LIST-WHEN-NOT-CONSP (IMPLIES (NOT (CONSP CUTIL::X)) (EQUAL (CUTIL::DUPE-LIST CUTIL::X) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST-OF-CONS (EQUAL (CUTIL::DUPE-LIST (CONS CUTIL::A CUTIL::X)) (CONS (CUTIL::DUPE CUTIL::A) (CUTIL::DUPE-LIST CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::TRUE-LISTP-OF-DUPE-LIST (EQUAL (TRUE-LISTP (CUTIL::DUPE-LIST CUTIL::X)) T) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST-WHEN-NOT-CONSP CUTIL::DUPE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::LEN-OF-DUPE-LIST (EQUAL (LEN (CUTIL::DUPE-LIST CUTIL::X)) (LEN CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST-WHEN-NOT-CONSP CUTIL::DUPE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CONSP-OF-DUPE-LIST (EQUAL (CONSP (CUTIL::DUPE-LIST CUTIL::X)) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST-WHEN-NOT-CONSP CUTIL::DUPE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CAR-OF-DUPE-LIST (EQUAL (CAR (CUTIL::DUPE-LIST CUTIL::X)) (IF (CONSP CUTIL::X) (CUTIL::DUPE (CAR CUTIL::X)) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST-WHEN-NOT-CONSP CUTIL::DUPE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CDR-OF-DUPE-LIST (EQUAL (CDR (CUTIL::DUPE-LIST CUTIL::X)) (CUTIL::DUPE-LIST (CDR CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST-WHEN-NOT-CONSP CUTIL::DUPE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST-UNDER-IFF (IFF (CUTIL::DUPE-LIST CUTIL::X) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST-WHEN-NOT-CONSP CUTIL::DUPE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST-OF-LIST-FIX (EQUAL (CUTIL::DUPE-LIST (LIST-FIX CUTIL::X)) (CUTIL::DUPE-LIST CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST-WHEN-NOT-CONSP CUTIL::DUPE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST-OF-APPEND (EQUAL (CUTIL::DUPE-LIST (APPEND CUTIL::X CUTIL::Y)) (APPEND (CUTIL::DUPE-LIST CUTIL::X) (CUTIL::DUPE-LIST CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST-WHEN-NOT-CONSP CUTIL::DUPE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST-OF-REV (EQUAL (CUTIL::DUPE-LIST (REV CUTIL::X)) (REV (CUTIL::DUPE-LIST CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST-OF-APPEND CUTIL::DUPE-LIST-WHEN-NOT-CONSP CUTIL::DUPE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST-OF-REVAPPEND (EQUAL (CUTIL::DUPE-LIST (REVAPPEND CUTIL::X CUTIL::Y)) (REVAPPEND (CUTIL::DUPE-LIST CUTIL::X) (CUTIL::DUPE-LIST CUTIL::Y))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST-OF-APPEND CUTIL::DUPE-LIST-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::NTHCDR-OF-DUPE-LIST (EQUAL (NTHCDR CUTIL::N (CUTIL::DUPE-LIST CUTIL::X)) (CUTIL::DUPE-LIST (NTHCDR CUTIL::N CUTIL::X))) :HINTS (("Goal" :INDUCT (NTHCDR CUTIL::N CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (NTHCDR CUTIL::DUPE-LIST-WHEN-NOT-CONSP CUTIL::DUPE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MEMBER-EQUAL-OF-DUPE-IN-DUPE-LIST-WHEN-MEMBER-EQUAL (IMPLIES (MEMBER-EQUAL CUTIL::A (DOUBLE-REWRITE CUTIL::X)) (MEMBER-EQUAL (CUTIL::DUPE CUTIL::A) (CUTIL::DUPE-LIST CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (MEMBER-EQUAL CUTIL::DUPE-LIST-WHEN-NOT-CONSP CUTIL::DUPE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SUBSETP-EQUAL-OF-DUPE-LISTS-WHEN-SUBSETP-EQUAL (IMPLIES (SUBSETP-EQUAL (DOUBLE-REWRITE CUTIL::X) (DOUBLE-REWRITE CUTIL::Y)) (SUBSETP-EQUAL (CUTIL::DUPE-LIST CUTIL::X) (CUTIL::DUPE-LIST CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (SUBSETP-EQUAL CUTIL::MEMBER-EQUAL-OF-DUPE-IN-DUPE-LIST-WHEN-MEMBER-EQUAL CUTIL::DUPE-LIST-WHEN-NOT-CONSP CUTIL::DUPE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST-EXEC-REMOVAL (EQUAL (CUTIL::DUPE-LIST-EXEC CUTIL::X CUTIL::ACC) (REVAPPEND (CUTIL::DUPE-LIST CUTIL::X) CUTIL::ACC)) :HINTS (("Goal" :INDUCT (CUTIL::DUPE-LIST-EXEC CUTIL::X CUTIL::ACC) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST-EXEC CUTIL::DUPE-LIST-WHEN-NOT-CONSP CUTIL::DUPE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (VERIFY-GUARDS CUTIL::DUPE-LIST-EXEC :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST-EXEC)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (VERIFY-GUARDS CUTIL::DUPE-LIST :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST CUTIL::DUPE-LIST-EXEC-REMOVAL CUTIL::TRUE-LISTP-OF-DUPE-LIST REVERSE-REMOVAL REVAPPEND-REMOVAL REV-OF-APPEND REV-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (LOCAL (IN-THEORY (ENABLE CUTIL::DUPE-LIST CUTIL::DUPE-LIST-WHEN-NOT-CONSP CUTIL::DUPE-LIST-OF-CONS)))))) (RECORD-EXPANSION (MAKE-EVENT (LET* ((XDOC::NAME (QUOTE CUTIL::DUPE-LIST)) (XDOC::PARENTS (QUOTE (UNDOCUMENTED))) (XDOC::SHORT (QUOTE "@(call DUPE-LIST) maps @(see CUTIL::DUPE) across a list.")) (XDOC::EXTENSION (QUOTE NIL)) (XDOC::WRLD (W STATE)) (XDOC::TRIPS (REVERSED-WORLD-SINCE-EVENT XDOC::WRLD (QUOTE (TABLE INTRO-TABLE :MARK (QUOTE CUTIL::DUPE-LIST))) NIL)) (XDOC::INFO (REVERSE (NEW-FORMULA-INFO XDOC::TRIPS XDOC::WRLD NIL))) (XDOC::AUTODOC (XDOC::FORMULA-INFO-TO-DEFS (NOT XDOC::EXTENSION) XDOC::INFO)) (XDOC::LONG (CONCATENATE (QUOTE STRING) (QUOTE "<p>This is an ordinary @(see defprojection).</p>") (COERCE (LIST #\Newline #\Newline) (QUOTE STRING)) XDOC::AUTODOC))) (IF XDOC::EXTENSION (CONS (QUOTE XDOC-EXTEND) (CONS XDOC::EXTENSION (CONS XDOC::LONG (QUOTE NIL)))) (CONS (QUOTE DEFXDOC) (CONS XDOC::NAME (CONS (QUOTE :PARENTS) (CONS XDOC::PARENTS (CONS (QUOTE :SHORT) (CONS XDOC::SHORT (CONS (QUOTE :LONG) (CONS XDOC::LONG (QUOTE NIL)))))))))))) (WITH-OUTPUT :OFF (EVENT SUMMARY) (PROGN (TABLE XDOC (QUOTE DOC) (CONS (QUOTE ((:NAME . CUTIL::DUPE-LIST) (:BASE-PKG . CUTIL::ACL2-PKG-WITNESS) (:PARENTS UNDOCUMENTED) (:SHORT . "@(call DUPE-LIST) maps @(see CUTIL::DUPE) across a list.") (:LONG . "<p>This is an ordinary @(see defprojection).</p>

<h3>Definitions and Theorems</h3>@(def |CUTIL|::|DUPE-LIST-EXEC|)
@(def |CUTIL|::|DUPE-LIST|)
@(def |CUTIL|::|DUPE-LIST-WHEN-NOT-CONSP|)
@(def |CUTIL|::|DUPE-LIST-OF-CONS|)
@(def |CUTIL|::|TRUE-LISTP-OF-DUPE-LIST|)
@(def |CUTIL|::|LEN-OF-DUPE-LIST|)
@(def |CUTIL|::|CONSP-OF-DUPE-LIST|)
@(def |CUTIL|::|CAR-OF-DUPE-LIST|)
@(def |CUTIL|::|CDR-OF-DUPE-LIST|)
@(def |CUTIL|::|DUPE-LIST-UNDER-IFF|)
@(def |CUTIL|::|DUPE-LIST-OF-LIST-FIX|)
@(def |CUTIL|::|DUPE-LIST-OF-APPEND|)
@(def |CUTIL|::|DUPE-LIST-OF-REV|)
@(def |CUTIL|::|DUPE-LIST-OF-REVAPPEND|)
@(def |CUTIL|::|NTHCDR-OF-DUPE-LIST|)
@(def |CUTIL|::|MEMBER-EQUAL-OF-DUPE-IN-DUPE-LIST-WHEN-MEMBER-EQUAL|)
@(def |CUTIL|::|SUBSETP-EQUAL-OF-DUPE-LISTS-WHEN-SUBSETP-EQUAL|)
@(def |CUTIL|::|DUPE-LIST-EXEC-REMOVAL|)") (:FROM . "[books]/cutil/defprojection-tests.lisp"))) (XDOC::GET-XDOC-TABLE WORLD))) (VALUE-TRIPLE (QUOTE (DEFXDOC CUTIL::DUPE-LIST)))))) (VALUE-TRIPLE (QUOTE CUTIL::DUPE-LIST))))) (7 RECORD-EXPANSION (CUTIL::DEFPROJECTION CUTIL::DUPE-LIST2 (CUTIL::X) (CUTIL::DUPE CUTIL::X) :OPTIMIZE T) (WITH-OUTPUT :STACK :PUSH :OFF :ALL :ON ERROR (PROGN (TABLE INTRO-TABLE :MARK (QUOTE CUTIL::DUPE-LIST2)) (RECORD-EXPANSION (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (LOGIC) (DEFUND CUTIL::DUPE-LIST2-EXEC (CUTIL::X CUTIL::ACC) (DECLARE (XARGS :GUARD T :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (IF (CONSP CUTIL::X) (CUTIL::DUPE-LIST2-EXEC (CDR CUTIL::X) (CONS (CUTIL::DUPE (CAR CUTIL::X)) CUTIL::ACC)) CUTIL::ACC)) (DEFUND CUTIL::DUPE-LIST2 (CUTIL::X) (DECLARE (XARGS :GUARD T :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (MBE :LOGIC (IF (CONSP CUTIL::X) (CONS (CUTIL::DUPE (CAR CUTIL::X)) (CUTIL::DUPE-LIST2 (CDR CUTIL::X))) NIL) :EXEC (REVERSE (CUTIL::DUPE-LIST2-EXEC CUTIL::X NIL)))) (SET-INHIBIT-WARNINGS "disable") (LOCAL (MAKE-EVENT (IF (CUTIL::IS-THEOREM-P (QUOTE CUTIL::DUPE-LIST2-NIL-PRESERVINGP-LEMMA) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (DEFTHM CUTIL::DUPE-LIST2-NIL-PRESERVINGP-LEMMA (OR (EQUAL (ALISTP CUTIL::X) T) (EQUAL (ALISTP CUTIL::X) NIL)) :RULE-CLASSES :TYPE-PRESCRIPTION :HINTS (("Goal" :IN-THEORY (QUOTE ((:TYPE-PRESCRIPTION ALISTP))))))))))) (DEFTHM CUTIL::DUPE-LIST2-WHEN-NOT-CONSP (IMPLIES (NOT (CONSP CUTIL::X)) (EQUAL (CUTIL::DUPE-LIST2 CUTIL::X) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST2)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST2-OF-CONS (EQUAL (CUTIL::DUPE-LIST2 (CONS CUTIL::A CUTIL::X)) (CONS (CUTIL::DUPE CUTIL::A) (CUTIL::DUPE-LIST2 CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST2)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::TRUE-LISTP-OF-DUPE-LIST2 (EQUAL (TRUE-LISTP (CUTIL::DUPE-LIST2 CUTIL::X)) T) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST2-WHEN-NOT-CONSP CUTIL::DUPE-LIST2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::LEN-OF-DUPE-LIST2 (EQUAL (LEN (CUTIL::DUPE-LIST2 CUTIL::X)) (LEN CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST2-WHEN-NOT-CONSP CUTIL::DUPE-LIST2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CONSP-OF-DUPE-LIST2 (EQUAL (CONSP (CUTIL::DUPE-LIST2 CUTIL::X)) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST2-WHEN-NOT-CONSP CUTIL::DUPE-LIST2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CAR-OF-DUPE-LIST2 (EQUAL (CAR (CUTIL::DUPE-LIST2 CUTIL::X)) (IF (CONSP CUTIL::X) (CUTIL::DUPE (CAR CUTIL::X)) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST2-WHEN-NOT-CONSP CUTIL::DUPE-LIST2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CDR-OF-DUPE-LIST2 (EQUAL (CDR (CUTIL::DUPE-LIST2 CUTIL::X)) (CUTIL::DUPE-LIST2 (CDR CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST2-WHEN-NOT-CONSP CUTIL::DUPE-LIST2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST2-UNDER-IFF (IFF (CUTIL::DUPE-LIST2 CUTIL::X) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST2-WHEN-NOT-CONSP CUTIL::DUPE-LIST2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST2-OF-LIST-FIX (EQUAL (CUTIL::DUPE-LIST2 (LIST-FIX CUTIL::X)) (CUTIL::DUPE-LIST2 CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST2-WHEN-NOT-CONSP CUTIL::DUPE-LIST2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST2-OF-APPEND (EQUAL (CUTIL::DUPE-LIST2 (APPEND CUTIL::X CUTIL::Y)) (APPEND (CUTIL::DUPE-LIST2 CUTIL::X) (CUTIL::DUPE-LIST2 CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST2-WHEN-NOT-CONSP CUTIL::DUPE-LIST2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST2-OF-REV (EQUAL (CUTIL::DUPE-LIST2 (REV CUTIL::X)) (REV (CUTIL::DUPE-LIST2 CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST2-OF-APPEND CUTIL::DUPE-LIST2-WHEN-NOT-CONSP CUTIL::DUPE-LIST2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST2-OF-REVAPPEND (EQUAL (CUTIL::DUPE-LIST2 (REVAPPEND CUTIL::X CUTIL::Y)) (REVAPPEND (CUTIL::DUPE-LIST2 CUTIL::X) (CUTIL::DUPE-LIST2 CUTIL::Y))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST2-OF-APPEND CUTIL::DUPE-LIST2-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::NTHCDR-OF-DUPE-LIST2 (EQUAL (NTHCDR CUTIL::N (CUTIL::DUPE-LIST2 CUTIL::X)) (CUTIL::DUPE-LIST2 (NTHCDR CUTIL::N CUTIL::X))) :HINTS (("Goal" :INDUCT (NTHCDR CUTIL::N CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (NTHCDR CUTIL::DUPE-LIST2-WHEN-NOT-CONSP CUTIL::DUPE-LIST2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MEMBER-EQUAL-OF-DUPE-IN-DUPE-LIST2-WHEN-MEMBER-EQUAL (IMPLIES (MEMBER-EQUAL CUTIL::A (DOUBLE-REWRITE CUTIL::X)) (MEMBER-EQUAL (CUTIL::DUPE CUTIL::A) (CUTIL::DUPE-LIST2 CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (MEMBER-EQUAL CUTIL::DUPE-LIST2-WHEN-NOT-CONSP CUTIL::DUPE-LIST2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SUBSETP-EQUAL-OF-DUPE-LIST2S-WHEN-SUBSETP-EQUAL (IMPLIES (SUBSETP-EQUAL (DOUBLE-REWRITE CUTIL::X) (DOUBLE-REWRITE CUTIL::Y)) (SUBSETP-EQUAL (CUTIL::DUPE-LIST2 CUTIL::X) (CUTIL::DUPE-LIST2 CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (SUBSETP-EQUAL CUTIL::MEMBER-EQUAL-OF-DUPE-IN-DUPE-LIST2-WHEN-MEMBER-EQUAL CUTIL::DUPE-LIST2-WHEN-NOT-CONSP CUTIL::DUPE-LIST2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST2-EXEC-REMOVAL (EQUAL (CUTIL::DUPE-LIST2-EXEC CUTIL::X CUTIL::ACC) (REVAPPEND (CUTIL::DUPE-LIST2 CUTIL::X) CUTIL::ACC)) :HINTS (("Goal" :INDUCT (CUTIL::DUPE-LIST2-EXEC CUTIL::X CUTIL::ACC) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST2-EXEC CUTIL::DUPE-LIST2-WHEN-NOT-CONSP CUTIL::DUPE-LIST2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (VERIFY-GUARDS CUTIL::DUPE-LIST2-EXEC :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST2-EXEC)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (VERIFY-GUARDS CUTIL::DUPE-LIST2 :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST2 CUTIL::DUPE-LIST2-EXEC-REMOVAL CUTIL::TRUE-LISTP-OF-DUPE-LIST2 REVERSE-REMOVAL REVAPPEND-REMOVAL REV-OF-APPEND REV-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (PROGN (MAKE-EVENT (IF (GLOBAL-VAL (QUOTE INCLUDE-BOOK-PATH) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::DUPE-LIST2) (QUOTE (DEFUN CUTIL::DUPE-LIST2 (CUTIL::X) (NREVERSE (CUTIL::DUPE-LIST2-EXEC CUTIL::X NIL)))))))))) (DEFTTAG CUTIL::CUTIL-OPTIMIZE) (NEVER-MEMOIZE CUTIL::DUPE-LIST2-EXEC) (PROGN! (SET-RAW-MODE T) (DEFUN CUTIL::DUPE-LIST2 (CUTIL::X) (NREVERSE (CUTIL::DUPE-LIST2-EXEC CUTIL::X NIL)))) (DEFTTAG NIL)) (LOCAL (IN-THEORY (ENABLE CUTIL::DUPE-LIST2 CUTIL::DUPE-LIST2-WHEN-NOT-CONSP CUTIL::DUPE-LIST2-OF-CONS))))) (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (LOGIC) (DEFUND CUTIL::DUPE-LIST2-EXEC (CUTIL::X CUTIL::ACC) (DECLARE (XARGS :GUARD T :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (IF (CONSP CUTIL::X) (CUTIL::DUPE-LIST2-EXEC (CDR CUTIL::X) (CONS (CUTIL::DUPE (CAR CUTIL::X)) CUTIL::ACC)) CUTIL::ACC)) (DEFUND CUTIL::DUPE-LIST2 (CUTIL::X) (DECLARE (XARGS :GUARD T :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (MBE :LOGIC (IF (CONSP CUTIL::X) (CONS (CUTIL::DUPE (CAR CUTIL::X)) (CUTIL::DUPE-LIST2 (CDR CUTIL::X))) NIL) :EXEC (REVERSE (CUTIL::DUPE-LIST2-EXEC CUTIL::X NIL)))) (SET-INHIBIT-WARNINGS "disable") (RECORD-EXPANSION (LOCAL (MAKE-EVENT (IF (CUTIL::IS-THEOREM-P (QUOTE CUTIL::DUPE-LIST2-NIL-PRESERVINGP-LEMMA) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (DEFTHM CUTIL::DUPE-LIST2-NIL-PRESERVINGP-LEMMA (OR (EQUAL (ALISTP CUTIL::X) T) (EQUAL (ALISTP CUTIL::X) NIL)) :RULE-CLASSES :TYPE-PRESCRIPTION :HINTS (("Goal" :IN-THEORY (QUOTE ((:TYPE-PRESCRIPTION ALISTP))))))))))) (LOCAL (VALUE-TRIPLE :ELIDED))) (DEFTHM CUTIL::DUPE-LIST2-WHEN-NOT-CONSP (IMPLIES (NOT (CONSP CUTIL::X)) (EQUAL (CUTIL::DUPE-LIST2 CUTIL::X) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST2)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST2-OF-CONS (EQUAL (CUTIL::DUPE-LIST2 (CONS CUTIL::A CUTIL::X)) (CONS (CUTIL::DUPE CUTIL::A) (CUTIL::DUPE-LIST2 CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST2)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::TRUE-LISTP-OF-DUPE-LIST2 (EQUAL (TRUE-LISTP (CUTIL::DUPE-LIST2 CUTIL::X)) T) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST2-WHEN-NOT-CONSP CUTIL::DUPE-LIST2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::LEN-OF-DUPE-LIST2 (EQUAL (LEN (CUTIL::DUPE-LIST2 CUTIL::X)) (LEN CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST2-WHEN-NOT-CONSP CUTIL::DUPE-LIST2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CONSP-OF-DUPE-LIST2 (EQUAL (CONSP (CUTIL::DUPE-LIST2 CUTIL::X)) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST2-WHEN-NOT-CONSP CUTIL::DUPE-LIST2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CAR-OF-DUPE-LIST2 (EQUAL (CAR (CUTIL::DUPE-LIST2 CUTIL::X)) (IF (CONSP CUTIL::X) (CUTIL::DUPE (CAR CUTIL::X)) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST2-WHEN-NOT-CONSP CUTIL::DUPE-LIST2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CDR-OF-DUPE-LIST2 (EQUAL (CDR (CUTIL::DUPE-LIST2 CUTIL::X)) (CUTIL::DUPE-LIST2 (CDR CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST2-WHEN-NOT-CONSP CUTIL::DUPE-LIST2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST2-UNDER-IFF (IFF (CUTIL::DUPE-LIST2 CUTIL::X) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST2-WHEN-NOT-CONSP CUTIL::DUPE-LIST2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST2-OF-LIST-FIX (EQUAL (CUTIL::DUPE-LIST2 (LIST-FIX CUTIL::X)) (CUTIL::DUPE-LIST2 CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST2-WHEN-NOT-CONSP CUTIL::DUPE-LIST2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST2-OF-APPEND (EQUAL (CUTIL::DUPE-LIST2 (APPEND CUTIL::X CUTIL::Y)) (APPEND (CUTIL::DUPE-LIST2 CUTIL::X) (CUTIL::DUPE-LIST2 CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST2-WHEN-NOT-CONSP CUTIL::DUPE-LIST2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST2-OF-REV (EQUAL (CUTIL::DUPE-LIST2 (REV CUTIL::X)) (REV (CUTIL::DUPE-LIST2 CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST2-OF-APPEND CUTIL::DUPE-LIST2-WHEN-NOT-CONSP CUTIL::DUPE-LIST2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST2-OF-REVAPPEND (EQUAL (CUTIL::DUPE-LIST2 (REVAPPEND CUTIL::X CUTIL::Y)) (REVAPPEND (CUTIL::DUPE-LIST2 CUTIL::X) (CUTIL::DUPE-LIST2 CUTIL::Y))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST2-OF-APPEND CUTIL::DUPE-LIST2-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::NTHCDR-OF-DUPE-LIST2 (EQUAL (NTHCDR CUTIL::N (CUTIL::DUPE-LIST2 CUTIL::X)) (CUTIL::DUPE-LIST2 (NTHCDR CUTIL::N CUTIL::X))) :HINTS (("Goal" :INDUCT (NTHCDR CUTIL::N CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (NTHCDR CUTIL::DUPE-LIST2-WHEN-NOT-CONSP CUTIL::DUPE-LIST2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MEMBER-EQUAL-OF-DUPE-IN-DUPE-LIST2-WHEN-MEMBER-EQUAL (IMPLIES (MEMBER-EQUAL CUTIL::A (DOUBLE-REWRITE CUTIL::X)) (MEMBER-EQUAL (CUTIL::DUPE CUTIL::A) (CUTIL::DUPE-LIST2 CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (MEMBER-EQUAL CUTIL::DUPE-LIST2-WHEN-NOT-CONSP CUTIL::DUPE-LIST2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SUBSETP-EQUAL-OF-DUPE-LIST2S-WHEN-SUBSETP-EQUAL (IMPLIES (SUBSETP-EQUAL (DOUBLE-REWRITE CUTIL::X) (DOUBLE-REWRITE CUTIL::Y)) (SUBSETP-EQUAL (CUTIL::DUPE-LIST2 CUTIL::X) (CUTIL::DUPE-LIST2 CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (SUBSETP-EQUAL CUTIL::MEMBER-EQUAL-OF-DUPE-IN-DUPE-LIST2-WHEN-MEMBER-EQUAL CUTIL::DUPE-LIST2-WHEN-NOT-CONSP CUTIL::DUPE-LIST2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST2-EXEC-REMOVAL (EQUAL (CUTIL::DUPE-LIST2-EXEC CUTIL::X CUTIL::ACC) (REVAPPEND (CUTIL::DUPE-LIST2 CUTIL::X) CUTIL::ACC)) :HINTS (("Goal" :INDUCT (CUTIL::DUPE-LIST2-EXEC CUTIL::X CUTIL::ACC) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST2-EXEC CUTIL::DUPE-LIST2-WHEN-NOT-CONSP CUTIL::DUPE-LIST2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (VERIFY-GUARDS CUTIL::DUPE-LIST2-EXEC :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST2-EXEC)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (VERIFY-GUARDS CUTIL::DUPE-LIST2 :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST2 CUTIL::DUPE-LIST2-EXEC-REMOVAL CUTIL::TRUE-LISTP-OF-DUPE-LIST2 REVERSE-REMOVAL REVAPPEND-REMOVAL REV-OF-APPEND REV-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (RECORD-EXPANSION (PROGN (MAKE-EVENT (IF (GLOBAL-VAL (QUOTE INCLUDE-BOOK-PATH) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::DUPE-LIST2) (QUOTE (DEFUN CUTIL::DUPE-LIST2 (CUTIL::X) (NREVERSE (CUTIL::DUPE-LIST2-EXEC CUTIL::X NIL)))))))))) (DEFTTAG CUTIL::CUTIL-OPTIMIZE) (NEVER-MEMOIZE CUTIL::DUPE-LIST2-EXEC) (PROGN! (SET-RAW-MODE T) (DEFUN CUTIL::DUPE-LIST2 (CUTIL::X) (NREVERSE (CUTIL::DUPE-LIST2-EXEC CUTIL::X NIL)))) (DEFTTAG NIL)) (PROGN (RECORD-EXPANSION (MAKE-EVENT (IF (GLOBAL-VAL (QUOTE INCLUDE-BOOK-PATH) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::DUPE-LIST2) (QUOTE (DEFUN CUTIL::DUPE-LIST2 (CUTIL::X) (NREVERSE (CUTIL::DUPE-LIST2-EXEC CUTIL::X NIL)))))))))) (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::DUPE-LIST2) (QUOTE (DEFUN CUTIL::DUPE-LIST2 (CUTIL::X) (NREVERSE (CUTIL::DUPE-LIST2-EXEC CUTIL::X NIL))))))) (DEFTTAG CUTIL::CUTIL-OPTIMIZE) (RECORD-EXPANSION (NEVER-MEMOIZE CUTIL::DUPE-LIST2-EXEC) (MAKE-EVENT (PROG2$ (NEVER-MEMOIZE-FN (QUOTE CUTIL::DUPE-LIST2-EXEC)) (QUOTE (VALUE-TRIPLE :INVISIBLE))) :CHECK-EXPANSION (VALUE-TRIPLE :INVISIBLE))) (PROGN! (SET-RAW-MODE T) (DEFUN CUTIL::DUPE-LIST2 (CUTIL::X) (NREVERSE (CUTIL::DUPE-LIST2-EXEC CUTIL::X NIL)))) (DEFTTAG NIL))) (LOCAL (IN-THEORY (ENABLE CUTIL::DUPE-LIST2 CUTIL::DUPE-LIST2-WHEN-NOT-CONSP CUTIL::DUPE-LIST2-OF-CONS)))))) (RECORD-EXPANSION (MAKE-EVENT (LET* ((XDOC::NAME (QUOTE CUTIL::DUPE-LIST2)) (XDOC::PARENTS (QUOTE (UNDOCUMENTED))) (XDOC::SHORT (QUOTE "@(call DUPE-LIST2) maps @(see CUTIL::DUPE) across a list.")) (XDOC::EXTENSION (QUOTE NIL)) (XDOC::WRLD (W STATE)) (XDOC::TRIPS (REVERSED-WORLD-SINCE-EVENT XDOC::WRLD (QUOTE (TABLE INTRO-TABLE :MARK (QUOTE CUTIL::DUPE-LIST2))) NIL)) (XDOC::INFO (REVERSE (NEW-FORMULA-INFO XDOC::TRIPS XDOC::WRLD NIL))) (XDOC::AUTODOC (XDOC::FORMULA-INFO-TO-DEFS (NOT XDOC::EXTENSION) XDOC::INFO)) (XDOC::LONG (CONCATENATE (QUOTE STRING) (QUOTE "<p>This is an ordinary @(see defprojection).</p>") (COERCE (LIST #\Newline #\Newline) (QUOTE STRING)) XDOC::AUTODOC))) (IF XDOC::EXTENSION (CONS (QUOTE XDOC-EXTEND) (CONS XDOC::EXTENSION (CONS XDOC::LONG (QUOTE NIL)))) (CONS (QUOTE DEFXDOC) (CONS XDOC::NAME (CONS (QUOTE :PARENTS) (CONS XDOC::PARENTS (CONS (QUOTE :SHORT) (CONS XDOC::SHORT (CONS (QUOTE :LONG) (CONS XDOC::LONG (QUOTE NIL)))))))))))) (WITH-OUTPUT :OFF (EVENT SUMMARY) (PROGN (TABLE XDOC (QUOTE DOC) (CONS (QUOTE ((:NAME . CUTIL::DUPE-LIST2) (:BASE-PKG . CUTIL::ACL2-PKG-WITNESS) (:PARENTS UNDOCUMENTED) (:SHORT . "@(call DUPE-LIST2) maps @(see CUTIL::DUPE) across a list.") (:LONG . "<p>This is an ordinary @(see defprojection).</p>

<h3>Definitions and Theorems</h3>@(def |CUTIL|::|DUPE-LIST2-EXEC|)
@(def |CUTIL|::|DUPE-LIST2|)
@(def |CUTIL|::|DUPE-LIST2-WHEN-NOT-CONSP|)
@(def |CUTIL|::|DUPE-LIST2-OF-CONS|)
@(def |CUTIL|::|TRUE-LISTP-OF-DUPE-LIST2|)
@(def |CUTIL|::|LEN-OF-DUPE-LIST2|)
@(def |CUTIL|::|CONSP-OF-DUPE-LIST2|)
@(def |CUTIL|::|CAR-OF-DUPE-LIST2|)
@(def |CUTIL|::|CDR-OF-DUPE-LIST2|)
@(def |CUTIL|::|DUPE-LIST2-UNDER-IFF|)
@(def |CUTIL|::|DUPE-LIST2-OF-LIST-FIX|)
@(def |CUTIL|::|DUPE-LIST2-OF-APPEND|)
@(def |CUTIL|::|DUPE-LIST2-OF-REV|)
@(def |CUTIL|::|DUPE-LIST2-OF-REVAPPEND|)
@(def |CUTIL|::|NTHCDR-OF-DUPE-LIST2|)
@(def |CUTIL|::|MEMBER-EQUAL-OF-DUPE-IN-DUPE-LIST2-WHEN-MEMBER-EQUAL|)
@(def |CUTIL|::|SUBSETP-EQUAL-OF-DUPE-LIST2S-WHEN-SUBSETP-EQUAL|)
@(def |CUTIL|::|DUPE-LIST2-EXEC-REMOVAL|)") (:FROM . "[books]/cutil/defprojection-tests.lisp"))) (XDOC::GET-XDOC-TABLE WORLD))) (VALUE-TRIPLE (QUOTE (DEFXDOC CUTIL::DUPE-LIST2)))))) (VALUE-TRIPLE (QUOTE CUTIL::DUPE-LIST2))))) (8 RECORD-EXPANSION (CUTIL::DEFPROJECTION CUTIL::DUPE-LIST3 (CUTIL::X) (CUTIL::DUPE CUTIL::X) :VERIFY-GUARDS NIL) (WITH-OUTPUT :STACK :PUSH :OFF :ALL :ON ERROR (PROGN (TABLE INTRO-TABLE :MARK (QUOTE CUTIL::DUPE-LIST3)) (RECORD-EXPANSION (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (LOGIC) (DEFUND CUTIL::DUPE-LIST3-EXEC (CUTIL::X CUTIL::ACC) (DECLARE (XARGS :GUARD T :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (IF (CONSP CUTIL::X) (CUTIL::DUPE-LIST3-EXEC (CDR CUTIL::X) (CONS (CUTIL::DUPE (CAR CUTIL::X)) CUTIL::ACC)) CUTIL::ACC)) (DEFUND CUTIL::DUPE-LIST3 (CUTIL::X) (DECLARE (XARGS :GUARD T :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (MBE :LOGIC (IF (CONSP CUTIL::X) (CONS (CUTIL::DUPE (CAR CUTIL::X)) (CUTIL::DUPE-LIST3 (CDR CUTIL::X))) NIL) :EXEC (REVERSE (CUTIL::DUPE-LIST3-EXEC CUTIL::X NIL)))) (SET-INHIBIT-WARNINGS "disable") (LOCAL (MAKE-EVENT (IF (CUTIL::IS-THEOREM-P (QUOTE CUTIL::DUPE-LIST3-NIL-PRESERVINGP-LEMMA) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (DEFTHM CUTIL::DUPE-LIST3-NIL-PRESERVINGP-LEMMA (OR (EQUAL (ALISTP CUTIL::X) T) (EQUAL (ALISTP CUTIL::X) NIL)) :RULE-CLASSES :TYPE-PRESCRIPTION :HINTS (("Goal" :IN-THEORY (QUOTE ((:TYPE-PRESCRIPTION ALISTP))))))))))) (DEFTHM CUTIL::DUPE-LIST3-WHEN-NOT-CONSP (IMPLIES (NOT (CONSP CUTIL::X)) (EQUAL (CUTIL::DUPE-LIST3 CUTIL::X) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST3)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST3-OF-CONS (EQUAL (CUTIL::DUPE-LIST3 (CONS CUTIL::A CUTIL::X)) (CONS (CUTIL::DUPE CUTIL::A) (CUTIL::DUPE-LIST3 CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST3)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::TRUE-LISTP-OF-DUPE-LIST3 (EQUAL (TRUE-LISTP (CUTIL::DUPE-LIST3 CUTIL::X)) T) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST3-WHEN-NOT-CONSP CUTIL::DUPE-LIST3-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::LEN-OF-DUPE-LIST3 (EQUAL (LEN (CUTIL::DUPE-LIST3 CUTIL::X)) (LEN CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST3-WHEN-NOT-CONSP CUTIL::DUPE-LIST3-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CONSP-OF-DUPE-LIST3 (EQUAL (CONSP (CUTIL::DUPE-LIST3 CUTIL::X)) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST3-WHEN-NOT-CONSP CUTIL::DUPE-LIST3-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CAR-OF-DUPE-LIST3 (EQUAL (CAR (CUTIL::DUPE-LIST3 CUTIL::X)) (IF (CONSP CUTIL::X) (CUTIL::DUPE (CAR CUTIL::X)) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST3-WHEN-NOT-CONSP CUTIL::DUPE-LIST3-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CDR-OF-DUPE-LIST3 (EQUAL (CDR (CUTIL::DUPE-LIST3 CUTIL::X)) (CUTIL::DUPE-LIST3 (CDR CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST3-WHEN-NOT-CONSP CUTIL::DUPE-LIST3-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST3-UNDER-IFF (IFF (CUTIL::DUPE-LIST3 CUTIL::X) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST3-WHEN-NOT-CONSP CUTIL::DUPE-LIST3-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST3-OF-LIST-FIX (EQUAL (CUTIL::DUPE-LIST3 (LIST-FIX CUTIL::X)) (CUTIL::DUPE-LIST3 CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST3-WHEN-NOT-CONSP CUTIL::DUPE-LIST3-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST3-OF-APPEND (EQUAL (CUTIL::DUPE-LIST3 (APPEND CUTIL::X CUTIL::Y)) (APPEND (CUTIL::DUPE-LIST3 CUTIL::X) (CUTIL::DUPE-LIST3 CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST3-WHEN-NOT-CONSP CUTIL::DUPE-LIST3-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST3-OF-REV (EQUAL (CUTIL::DUPE-LIST3 (REV CUTIL::X)) (REV (CUTIL::DUPE-LIST3 CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST3-OF-APPEND CUTIL::DUPE-LIST3-WHEN-NOT-CONSP CUTIL::DUPE-LIST3-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST3-OF-REVAPPEND (EQUAL (CUTIL::DUPE-LIST3 (REVAPPEND CUTIL::X CUTIL::Y)) (REVAPPEND (CUTIL::DUPE-LIST3 CUTIL::X) (CUTIL::DUPE-LIST3 CUTIL::Y))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST3-OF-APPEND CUTIL::DUPE-LIST3-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::NTHCDR-OF-DUPE-LIST3 (EQUAL (NTHCDR CUTIL::N (CUTIL::DUPE-LIST3 CUTIL::X)) (CUTIL::DUPE-LIST3 (NTHCDR CUTIL::N CUTIL::X))) :HINTS (("Goal" :INDUCT (NTHCDR CUTIL::N CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (NTHCDR CUTIL::DUPE-LIST3-WHEN-NOT-CONSP CUTIL::DUPE-LIST3-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MEMBER-EQUAL-OF-DUPE-IN-DUPE-LIST3-WHEN-MEMBER-EQUAL (IMPLIES (MEMBER-EQUAL CUTIL::A (DOUBLE-REWRITE CUTIL::X)) (MEMBER-EQUAL (CUTIL::DUPE CUTIL::A) (CUTIL::DUPE-LIST3 CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (MEMBER-EQUAL CUTIL::DUPE-LIST3-WHEN-NOT-CONSP CUTIL::DUPE-LIST3-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SUBSETP-EQUAL-OF-DUPE-LIST3S-WHEN-SUBSETP-EQUAL (IMPLIES (SUBSETP-EQUAL (DOUBLE-REWRITE CUTIL::X) (DOUBLE-REWRITE CUTIL::Y)) (SUBSETP-EQUAL (CUTIL::DUPE-LIST3 CUTIL::X) (CUTIL::DUPE-LIST3 CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (SUBSETP-EQUAL CUTIL::MEMBER-EQUAL-OF-DUPE-IN-DUPE-LIST3-WHEN-MEMBER-EQUAL CUTIL::DUPE-LIST3-WHEN-NOT-CONSP CUTIL::DUPE-LIST3-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST3-EXEC-REMOVAL (EQUAL (CUTIL::DUPE-LIST3-EXEC CUTIL::X CUTIL::ACC) (REVAPPEND (CUTIL::DUPE-LIST3 CUTIL::X) CUTIL::ACC)) :HINTS (("Goal" :INDUCT (CUTIL::DUPE-LIST3-EXEC CUTIL::X CUTIL::ACC) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST3-EXEC CUTIL::DUPE-LIST3-WHEN-NOT-CONSP CUTIL::DUPE-LIST3-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (PROGN (MAKE-EVENT (IF (GLOBAL-VAL (QUOTE INCLUDE-BOOK-PATH) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::DUPE-LIST3) (QUOTE (DEFUN CUTIL::DUPE-LIST3 (CUTIL::X) (NREVERSE (CUTIL::DUPE-LIST3-EXEC CUTIL::X NIL)))))))))) (DEFTTAG CUTIL::CUTIL-OPTIMIZE) (NEVER-MEMOIZE CUTIL::DUPE-LIST3-EXEC) (PROGN! (SET-RAW-MODE T) (DEFUN CUTIL::DUPE-LIST3 (CUTIL::X) (NREVERSE (CUTIL::DUPE-LIST3-EXEC CUTIL::X NIL)))) (DEFTTAG NIL)) (LOCAL (IN-THEORY (ENABLE CUTIL::DUPE-LIST3 CUTIL::DUPE-LIST3-WHEN-NOT-CONSP CUTIL::DUPE-LIST3-OF-CONS))))) (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (LOGIC) (DEFUND CUTIL::DUPE-LIST3-EXEC (CUTIL::X CUTIL::ACC) (DECLARE (XARGS :GUARD T :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (IF (CONSP CUTIL::X) (CUTIL::DUPE-LIST3-EXEC (CDR CUTIL::X) (CONS (CUTIL::DUPE (CAR CUTIL::X)) CUTIL::ACC)) CUTIL::ACC)) (DEFUND CUTIL::DUPE-LIST3 (CUTIL::X) (DECLARE (XARGS :GUARD T :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (MBE :LOGIC (IF (CONSP CUTIL::X) (CONS (CUTIL::DUPE (CAR CUTIL::X)) (CUTIL::DUPE-LIST3 (CDR CUTIL::X))) NIL) :EXEC (REVERSE (CUTIL::DUPE-LIST3-EXEC CUTIL::X NIL)))) (SET-INHIBIT-WARNINGS "disable") (RECORD-EXPANSION (LOCAL (MAKE-EVENT (IF (CUTIL::IS-THEOREM-P (QUOTE CUTIL::DUPE-LIST3-NIL-PRESERVINGP-LEMMA) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (DEFTHM CUTIL::DUPE-LIST3-NIL-PRESERVINGP-LEMMA (OR (EQUAL (ALISTP CUTIL::X) T) (EQUAL (ALISTP CUTIL::X) NIL)) :RULE-CLASSES :TYPE-PRESCRIPTION :HINTS (("Goal" :IN-THEORY (QUOTE ((:TYPE-PRESCRIPTION ALISTP))))))))))) (LOCAL (VALUE-TRIPLE :ELIDED))) (DEFTHM CUTIL::DUPE-LIST3-WHEN-NOT-CONSP (IMPLIES (NOT (CONSP CUTIL::X)) (EQUAL (CUTIL::DUPE-LIST3 CUTIL::X) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST3)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST3-OF-CONS (EQUAL (CUTIL::DUPE-LIST3 (CONS CUTIL::A CUTIL::X)) (CONS (CUTIL::DUPE CUTIL::A) (CUTIL::DUPE-LIST3 CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST3)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::TRUE-LISTP-OF-DUPE-LIST3 (EQUAL (TRUE-LISTP (CUTIL::DUPE-LIST3 CUTIL::X)) T) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST3-WHEN-NOT-CONSP CUTIL::DUPE-LIST3-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::LEN-OF-DUPE-LIST3 (EQUAL (LEN (CUTIL::DUPE-LIST3 CUTIL::X)) (LEN CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST3-WHEN-NOT-CONSP CUTIL::DUPE-LIST3-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CONSP-OF-DUPE-LIST3 (EQUAL (CONSP (CUTIL::DUPE-LIST3 CUTIL::X)) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST3-WHEN-NOT-CONSP CUTIL::DUPE-LIST3-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CAR-OF-DUPE-LIST3 (EQUAL (CAR (CUTIL::DUPE-LIST3 CUTIL::X)) (IF (CONSP CUTIL::X) (CUTIL::DUPE (CAR CUTIL::X)) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST3-WHEN-NOT-CONSP CUTIL::DUPE-LIST3-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CDR-OF-DUPE-LIST3 (EQUAL (CDR (CUTIL::DUPE-LIST3 CUTIL::X)) (CUTIL::DUPE-LIST3 (CDR CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST3-WHEN-NOT-CONSP CUTIL::DUPE-LIST3-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST3-UNDER-IFF (IFF (CUTIL::DUPE-LIST3 CUTIL::X) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST3-WHEN-NOT-CONSP CUTIL::DUPE-LIST3-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST3-OF-LIST-FIX (EQUAL (CUTIL::DUPE-LIST3 (LIST-FIX CUTIL::X)) (CUTIL::DUPE-LIST3 CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST3-WHEN-NOT-CONSP CUTIL::DUPE-LIST3-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST3-OF-APPEND (EQUAL (CUTIL::DUPE-LIST3 (APPEND CUTIL::X CUTIL::Y)) (APPEND (CUTIL::DUPE-LIST3 CUTIL::X) (CUTIL::DUPE-LIST3 CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST3-WHEN-NOT-CONSP CUTIL::DUPE-LIST3-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST3-OF-REV (EQUAL (CUTIL::DUPE-LIST3 (REV CUTIL::X)) (REV (CUTIL::DUPE-LIST3 CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST3-OF-APPEND CUTIL::DUPE-LIST3-WHEN-NOT-CONSP CUTIL::DUPE-LIST3-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST3-OF-REVAPPEND (EQUAL (CUTIL::DUPE-LIST3 (REVAPPEND CUTIL::X CUTIL::Y)) (REVAPPEND (CUTIL::DUPE-LIST3 CUTIL::X) (CUTIL::DUPE-LIST3 CUTIL::Y))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST3-OF-APPEND CUTIL::DUPE-LIST3-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::NTHCDR-OF-DUPE-LIST3 (EQUAL (NTHCDR CUTIL::N (CUTIL::DUPE-LIST3 CUTIL::X)) (CUTIL::DUPE-LIST3 (NTHCDR CUTIL::N CUTIL::X))) :HINTS (("Goal" :INDUCT (NTHCDR CUTIL::N CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (NTHCDR CUTIL::DUPE-LIST3-WHEN-NOT-CONSP CUTIL::DUPE-LIST3-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MEMBER-EQUAL-OF-DUPE-IN-DUPE-LIST3-WHEN-MEMBER-EQUAL (IMPLIES (MEMBER-EQUAL CUTIL::A (DOUBLE-REWRITE CUTIL::X)) (MEMBER-EQUAL (CUTIL::DUPE CUTIL::A) (CUTIL::DUPE-LIST3 CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (MEMBER-EQUAL CUTIL::DUPE-LIST3-WHEN-NOT-CONSP CUTIL::DUPE-LIST3-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SUBSETP-EQUAL-OF-DUPE-LIST3S-WHEN-SUBSETP-EQUAL (IMPLIES (SUBSETP-EQUAL (DOUBLE-REWRITE CUTIL::X) (DOUBLE-REWRITE CUTIL::Y)) (SUBSETP-EQUAL (CUTIL::DUPE-LIST3 CUTIL::X) (CUTIL::DUPE-LIST3 CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (SUBSETP-EQUAL CUTIL::MEMBER-EQUAL-OF-DUPE-IN-DUPE-LIST3-WHEN-MEMBER-EQUAL CUTIL::DUPE-LIST3-WHEN-NOT-CONSP CUTIL::DUPE-LIST3-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::DUPE-LIST3-EXEC-REMOVAL (EQUAL (CUTIL::DUPE-LIST3-EXEC CUTIL::X CUTIL::ACC) (REVAPPEND (CUTIL::DUPE-LIST3 CUTIL::X) CUTIL::ACC)) :HINTS (("Goal" :INDUCT (CUTIL::DUPE-LIST3-EXEC CUTIL::X CUTIL::ACC) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::DUPE-LIST3-EXEC CUTIL::DUPE-LIST3-WHEN-NOT-CONSP CUTIL::DUPE-LIST3-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (RECORD-EXPANSION (PROGN (MAKE-EVENT (IF (GLOBAL-VAL (QUOTE INCLUDE-BOOK-PATH) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::DUPE-LIST3) (QUOTE (DEFUN CUTIL::DUPE-LIST3 (CUTIL::X) (NREVERSE (CUTIL::DUPE-LIST3-EXEC CUTIL::X NIL)))))))))) (DEFTTAG CUTIL::CUTIL-OPTIMIZE) (NEVER-MEMOIZE CUTIL::DUPE-LIST3-EXEC) (PROGN! (SET-RAW-MODE T) (DEFUN CUTIL::DUPE-LIST3 (CUTIL::X) (NREVERSE (CUTIL::DUPE-LIST3-EXEC CUTIL::X NIL)))) (DEFTTAG NIL)) (PROGN (RECORD-EXPANSION (MAKE-EVENT (IF (GLOBAL-VAL (QUOTE INCLUDE-BOOK-PATH) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::DUPE-LIST3) (QUOTE (DEFUN CUTIL::DUPE-LIST3 (CUTIL::X) (NREVERSE (CUTIL::DUPE-LIST3-EXEC CUTIL::X NIL)))))))))) (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::DUPE-LIST3) (QUOTE (DEFUN CUTIL::DUPE-LIST3 (CUTIL::X) (NREVERSE (CUTIL::DUPE-LIST3-EXEC CUTIL::X NIL))))))) (DEFTTAG CUTIL::CUTIL-OPTIMIZE) (RECORD-EXPANSION (NEVER-MEMOIZE CUTIL::DUPE-LIST3-EXEC) (MAKE-EVENT (PROG2$ (NEVER-MEMOIZE-FN (QUOTE CUTIL::DUPE-LIST3-EXEC)) (QUOTE (VALUE-TRIPLE :INVISIBLE))) :CHECK-EXPANSION (VALUE-TRIPLE :INVISIBLE))) (PROGN! (SET-RAW-MODE T) (DEFUN CUTIL::DUPE-LIST3 (CUTIL::X) (NREVERSE (CUTIL::DUPE-LIST3-EXEC CUTIL::X NIL)))) (DEFTTAG NIL))) (LOCAL (IN-THEORY (ENABLE CUTIL::DUPE-LIST3 CUTIL::DUPE-LIST3-WHEN-NOT-CONSP CUTIL::DUPE-LIST3-OF-CONS)))))) (RECORD-EXPANSION (MAKE-EVENT (LET* ((XDOC::NAME (QUOTE CUTIL::DUPE-LIST3)) (XDOC::PARENTS (QUOTE (UNDOCUMENTED))) (XDOC::SHORT (QUOTE "@(call DUPE-LIST3) maps @(see CUTIL::DUPE) across a list.")) (XDOC::EXTENSION (QUOTE NIL)) (XDOC::WRLD (W STATE)) (XDOC::TRIPS (REVERSED-WORLD-SINCE-EVENT XDOC::WRLD (QUOTE (TABLE INTRO-TABLE :MARK (QUOTE CUTIL::DUPE-LIST3))) NIL)) (XDOC::INFO (REVERSE (NEW-FORMULA-INFO XDOC::TRIPS XDOC::WRLD NIL))) (XDOC::AUTODOC (XDOC::FORMULA-INFO-TO-DEFS (NOT XDOC::EXTENSION) XDOC::INFO)) (XDOC::LONG (CONCATENATE (QUOTE STRING) (QUOTE "<p>This is an ordinary @(see defprojection).</p>") (COERCE (LIST #\Newline #\Newline) (QUOTE STRING)) XDOC::AUTODOC))) (IF XDOC::EXTENSION (CONS (QUOTE XDOC-EXTEND) (CONS XDOC::EXTENSION (CONS XDOC::LONG (QUOTE NIL)))) (CONS (QUOTE DEFXDOC) (CONS XDOC::NAME (CONS (QUOTE :PARENTS) (CONS XDOC::PARENTS (CONS (QUOTE :SHORT) (CONS XDOC::SHORT (CONS (QUOTE :LONG) (CONS XDOC::LONG (QUOTE NIL)))))))))))) (WITH-OUTPUT :OFF (EVENT SUMMARY) (PROGN (TABLE XDOC (QUOTE DOC) (CONS (QUOTE ((:NAME . CUTIL::DUPE-LIST3) (:BASE-PKG . CUTIL::ACL2-PKG-WITNESS) (:PARENTS UNDOCUMENTED) (:SHORT . "@(call DUPE-LIST3) maps @(see CUTIL::DUPE) across a list.") (:LONG . "<p>This is an ordinary @(see defprojection).</p>

<h3>Definitions and Theorems</h3>@(def |CUTIL|::|DUPE-LIST3-EXEC|)
@(def |CUTIL|::|DUPE-LIST3|)
@(def |CUTIL|::|DUPE-LIST3-WHEN-NOT-CONSP|)
@(def |CUTIL|::|DUPE-LIST3-OF-CONS|)
@(def |CUTIL|::|TRUE-LISTP-OF-DUPE-LIST3|)
@(def |CUTIL|::|LEN-OF-DUPE-LIST3|)
@(def |CUTIL|::|CONSP-OF-DUPE-LIST3|)
@(def |CUTIL|::|CAR-OF-DUPE-LIST3|)
@(def |CUTIL|::|CDR-OF-DUPE-LIST3|)
@(def |CUTIL|::|DUPE-LIST3-UNDER-IFF|)
@(def |CUTIL|::|DUPE-LIST3-OF-LIST-FIX|)
@(def |CUTIL|::|DUPE-LIST3-OF-APPEND|)
@(def |CUTIL|::|DUPE-LIST3-OF-REV|)
@(def |CUTIL|::|DUPE-LIST3-OF-REVAPPEND|)
@(def |CUTIL|::|NTHCDR-OF-DUPE-LIST3|)
@(def |CUTIL|::|MEMBER-EQUAL-OF-DUPE-IN-DUPE-LIST3-WHEN-MEMBER-EQUAL|)
@(def |CUTIL|::|SUBSETP-EQUAL-OF-DUPE-LIST3S-WHEN-SUBSETP-EQUAL|)
@(def |CUTIL|::|DUPE-LIST3-EXEC-REMOVAL|)") (:FROM . "[books]/cutil/defprojection-tests.lisp"))) (XDOC::GET-XDOC-TABLE WORLD))) (VALUE-TRIPLE (QUOTE (DEFXDOC CUTIL::DUPE-LIST3)))))) (VALUE-TRIPLE (QUOTE CUTIL::DUPE-LIST3))))) (9 RECORD-EXPANSION (CUTIL::DEFPROJECTION CUTIL::DUPE-LIST4 (CUTIL::X) (CUTIL::DUPE CUTIL::X) :MODE :PROGRAM) (WITH-OUTPUT :STACK :PUSH :OFF :ALL :ON ERROR (PROGN (TABLE INTRO-TABLE :MARK (QUOTE CUTIL::DUPE-LIST4)) (RECORD-EXPANSION (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (PROGRAM) (DEFUND CUTIL::DUPE-LIST4-EXEC (CUTIL::X CUTIL::ACC) (DECLARE (XARGS :GUARD T :MODE :PROGRAM :NORMALIZE NIL :VERIFY-GUARDS NIL)) (IF (CONSP CUTIL::X) (CUTIL::DUPE-LIST4-EXEC (CDR CUTIL::X) (CONS (CUTIL::DUPE (CAR CUTIL::X)) CUTIL::ACC)) CUTIL::ACC)) (DEFUND CUTIL::DUPE-LIST4 (CUTIL::X) (DECLARE (XARGS :GUARD T :MODE :PROGRAM :NORMALIZE NIL :VERIFY-GUARDS NIL)) (MBE :LOGIC (IF (CONSP CUTIL::X) (CONS (CUTIL::DUPE (CAR CUTIL::X)) (CUTIL::DUPE-LIST4 (CDR CUTIL::X))) NIL) :EXEC (REVERSE (CUTIL::DUPE-LIST4-EXEC CUTIL::X NIL)))) (PROGN (MAKE-EVENT (IF (GLOBAL-VAL (QUOTE INCLUDE-BOOK-PATH) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::DUPE-LIST4) (QUOTE (DEFUN CUTIL::DUPE-LIST4 (CUTIL::X) (NREVERSE (CUTIL::DUPE-LIST4-EXEC CUTIL::X NIL)))))))))) (DEFTTAG CUTIL::CUTIL-OPTIMIZE) (NEVER-MEMOIZE CUTIL::DUPE-LIST4-EXEC) (PROGN! (SET-RAW-MODE T) (DEFUN CUTIL::DUPE-LIST4 (CUTIL::X) (NREVERSE (CUTIL::DUPE-LIST4-EXEC CUTIL::X NIL)))) (DEFTTAG NIL)))) (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (PROGRAM) (DEFUND CUTIL::DUPE-LIST4-EXEC (CUTIL::X CUTIL::ACC) (DECLARE (XARGS :GUARD T :MODE :PROGRAM :NORMALIZE NIL :VERIFY-GUARDS NIL)) (IF (CONSP CUTIL::X) (CUTIL::DUPE-LIST4-EXEC (CDR CUTIL::X) (CONS (CUTIL::DUPE (CAR CUTIL::X)) CUTIL::ACC)) CUTIL::ACC)) (DEFUND CUTIL::DUPE-LIST4 (CUTIL::X) (DECLARE (XARGS :GUARD T :MODE :PROGRAM :NORMALIZE NIL :VERIFY-GUARDS NIL)) (MBE :LOGIC (IF (CONSP CUTIL::X) (CONS (CUTIL::DUPE (CAR CUTIL::X)) (CUTIL::DUPE-LIST4 (CDR CUTIL::X))) NIL) :EXEC (REVERSE (CUTIL::DUPE-LIST4-EXEC CUTIL::X NIL)))) (RECORD-EXPANSION (PROGN (MAKE-EVENT (IF (GLOBAL-VAL (QUOTE INCLUDE-BOOK-PATH) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::DUPE-LIST4) (QUOTE (DEFUN CUTIL::DUPE-LIST4 (CUTIL::X) (NREVERSE (CUTIL::DUPE-LIST4-EXEC CUTIL::X NIL)))))))))) (DEFTTAG CUTIL::CUTIL-OPTIMIZE) (NEVER-MEMOIZE CUTIL::DUPE-LIST4-EXEC) (PROGN! (SET-RAW-MODE T) (DEFUN CUTIL::DUPE-LIST4 (CUTIL::X) (NREVERSE (CUTIL::DUPE-LIST4-EXEC CUTIL::X NIL)))) (DEFTTAG NIL)) (PROGN (RECORD-EXPANSION (MAKE-EVENT (IF (GLOBAL-VAL (QUOTE INCLUDE-BOOK-PATH) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::DUPE-LIST4) (QUOTE (DEFUN CUTIL::DUPE-LIST4 (CUTIL::X) (NREVERSE (CUTIL::DUPE-LIST4-EXEC CUTIL::X NIL)))))))))) (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::DUPE-LIST4) (QUOTE (DEFUN CUTIL::DUPE-LIST4 (CUTIL::X) (NREVERSE (CUTIL::DUPE-LIST4-EXEC CUTIL::X NIL))))))) (DEFTTAG CUTIL::CUTIL-OPTIMIZE) (RECORD-EXPANSION (NEVER-MEMOIZE CUTIL::DUPE-LIST4-EXEC) (MAKE-EVENT (PROG2$ (NEVER-MEMOIZE-FN (QUOTE CUTIL::DUPE-LIST4-EXEC)) (QUOTE (VALUE-TRIPLE :INVISIBLE))) :CHECK-EXPANSION (VALUE-TRIPLE :INVISIBLE))) (PROGN! (SET-RAW-MODE T) (DEFUN CUTIL::DUPE-LIST4 (CUTIL::X) (NREVERSE (CUTIL::DUPE-LIST4-EXEC CUTIL::X NIL)))) (DEFTTAG NIL)))))) (RECORD-EXPANSION (MAKE-EVENT (LET* ((XDOC::NAME (QUOTE CUTIL::DUPE-LIST4)) (XDOC::PARENTS (QUOTE (UNDOCUMENTED))) (XDOC::SHORT (QUOTE "@(call DUPE-LIST4) maps @(see CUTIL::DUPE) across a list.")) (XDOC::EXTENSION (QUOTE NIL)) (XDOC::WRLD (W STATE)) (XDOC::TRIPS (REVERSED-WORLD-SINCE-EVENT XDOC::WRLD (QUOTE (TABLE INTRO-TABLE :MARK (QUOTE CUTIL::DUPE-LIST4))) NIL)) (XDOC::INFO (REVERSE (NEW-FORMULA-INFO XDOC::TRIPS XDOC::WRLD NIL))) (XDOC::AUTODOC (XDOC::FORMULA-INFO-TO-DEFS (NOT XDOC::EXTENSION) XDOC::INFO)) (XDOC::LONG (CONCATENATE (QUOTE STRING) (QUOTE "<p>This is an ordinary @(see defprojection).</p>") (COERCE (LIST #\Newline #\Newline) (QUOTE STRING)) XDOC::AUTODOC))) (IF XDOC::EXTENSION (CONS (QUOTE XDOC-EXTEND) (CONS XDOC::EXTENSION (CONS XDOC::LONG (QUOTE NIL)))) (CONS (QUOTE DEFXDOC) (CONS XDOC::NAME (CONS (QUOTE :PARENTS) (CONS XDOC::PARENTS (CONS (QUOTE :SHORT) (CONS XDOC::SHORT (CONS (QUOTE :LONG) (CONS XDOC::LONG (QUOTE NIL)))))))))))) (WITH-OUTPUT :OFF (EVENT SUMMARY) (PROGN (TABLE XDOC (QUOTE DOC) (CONS (QUOTE ((:NAME . CUTIL::DUPE-LIST4) (:BASE-PKG . CUTIL::ACL2-PKG-WITNESS) (:PARENTS UNDOCUMENTED) (:SHORT . "@(call DUPE-LIST4) maps @(see CUTIL::DUPE) across a list.") (:LONG . "<p>This is an ordinary @(see defprojection).</p>

<h3>Definitions and Theorems</h3>@(def |CUTIL|::|DUPE-LIST4-EXEC|)
@(def |CUTIL|::|DUPE-LIST4|)") (:FROM . "[books]/cutil/defprojection-tests.lisp"))) (XDOC::GET-XDOC-TABLE WORLD))) (VALUE-TRIPLE (QUOTE (DEFXDOC CUTIL::DUPE-LIST4)))))) (VALUE-TRIPLE (QUOTE CUTIL::DUPE-LIST4))))) (12 RECORD-EXPANSION (CUTIL::DEFPROJECTION CUTIL::SLOW-SQUARE-LIST (CUTIL::X) (CUTIL::SQUARE CUTIL::X) :GUARD (INTEGER-LISTP CUTIL::X) :OPTIMIZE NIL) (WITH-OUTPUT :STACK :PUSH :OFF :ALL :ON ERROR (PROGN (TABLE INTRO-TABLE :MARK (QUOTE CUTIL::SLOW-SQUARE-LIST)) (RECORD-EXPANSION (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (LOGIC) (DEFUND CUTIL::SLOW-SQUARE-LIST-EXEC (CUTIL::X CUTIL::ACC) (DECLARE (XARGS :GUARD (INTEGER-LISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (IF (CONSP CUTIL::X) (CUTIL::SLOW-SQUARE-LIST-EXEC (CDR CUTIL::X) (CONS (CUTIL::SQUARE (CAR CUTIL::X)) CUTIL::ACC)) CUTIL::ACC)) (DEFUND CUTIL::SLOW-SQUARE-LIST (CUTIL::X) (DECLARE (XARGS :GUARD (INTEGER-LISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (MBE :LOGIC (IF (CONSP CUTIL::X) (CONS (CUTIL::SQUARE (CAR CUTIL::X)) (CUTIL::SLOW-SQUARE-LIST (CDR CUTIL::X))) NIL) :EXEC (REVERSE (CUTIL::SLOW-SQUARE-LIST-EXEC CUTIL::X NIL)))) (SET-INHIBIT-WARNINGS "disable") (LOCAL (MAKE-EVENT (IF (CUTIL::IS-THEOREM-P (QUOTE CUTIL::SLOW-SQUARE-LIST-NIL-PRESERVINGP-LEMMA) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (DEFTHM CUTIL::SLOW-SQUARE-LIST-NIL-PRESERVINGP-LEMMA (OR (EQUAL (ALISTP CUTIL::X) T) (EQUAL (ALISTP CUTIL::X) NIL)) :RULE-CLASSES :TYPE-PRESCRIPTION :HINTS (("Goal" :IN-THEORY (QUOTE ((:TYPE-PRESCRIPTION ALISTP))))))))))) (DEFTHM CUTIL::SLOW-SQUARE-LIST-WHEN-NOT-CONSP (IMPLIES (NOT (CONSP CUTIL::X)) (EQUAL (CUTIL::SLOW-SQUARE-LIST CUTIL::X) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SLOW-SQUARE-LIST)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SLOW-SQUARE-LIST-OF-CONS (EQUAL (CUTIL::SLOW-SQUARE-LIST (CONS CUTIL::A CUTIL::X)) (CONS (CUTIL::SQUARE CUTIL::A) (CUTIL::SLOW-SQUARE-LIST CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SLOW-SQUARE-LIST)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::TRUE-LISTP-OF-SLOW-SQUARE-LIST (EQUAL (TRUE-LISTP (CUTIL::SLOW-SQUARE-LIST CUTIL::X)) T) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SLOW-SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SLOW-SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::LEN-OF-SLOW-SQUARE-LIST (EQUAL (LEN (CUTIL::SLOW-SQUARE-LIST CUTIL::X)) (LEN CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SLOW-SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SLOW-SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CONSP-OF-SLOW-SQUARE-LIST (EQUAL (CONSP (CUTIL::SLOW-SQUARE-LIST CUTIL::X)) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SLOW-SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SLOW-SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CAR-OF-SLOW-SQUARE-LIST (EQUAL (CAR (CUTIL::SLOW-SQUARE-LIST CUTIL::X)) (IF (CONSP CUTIL::X) (CUTIL::SQUARE (CAR CUTIL::X)) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SLOW-SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SLOW-SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CDR-OF-SLOW-SQUARE-LIST (EQUAL (CDR (CUTIL::SLOW-SQUARE-LIST CUTIL::X)) (CUTIL::SLOW-SQUARE-LIST (CDR CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SLOW-SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SLOW-SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SLOW-SQUARE-LIST-UNDER-IFF (IFF (CUTIL::SLOW-SQUARE-LIST CUTIL::X) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SLOW-SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SLOW-SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SLOW-SQUARE-LIST-OF-LIST-FIX (EQUAL (CUTIL::SLOW-SQUARE-LIST (LIST-FIX CUTIL::X)) (CUTIL::SLOW-SQUARE-LIST CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SLOW-SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SLOW-SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SLOW-SQUARE-LIST-OF-APPEND (EQUAL (CUTIL::SLOW-SQUARE-LIST (APPEND CUTIL::X CUTIL::Y)) (APPEND (CUTIL::SLOW-SQUARE-LIST CUTIL::X) (CUTIL::SLOW-SQUARE-LIST CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SLOW-SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SLOW-SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SLOW-SQUARE-LIST-OF-REV (EQUAL (CUTIL::SLOW-SQUARE-LIST (REV CUTIL::X)) (REV (CUTIL::SLOW-SQUARE-LIST CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SLOW-SQUARE-LIST-OF-APPEND CUTIL::SLOW-SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SLOW-SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SLOW-SQUARE-LIST-OF-REVAPPEND (EQUAL (CUTIL::SLOW-SQUARE-LIST (REVAPPEND CUTIL::X CUTIL::Y)) (REVAPPEND (CUTIL::SLOW-SQUARE-LIST CUTIL::X) (CUTIL::SLOW-SQUARE-LIST CUTIL::Y))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SLOW-SQUARE-LIST-OF-APPEND CUTIL::SLOW-SQUARE-LIST-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::NTHCDR-OF-SLOW-SQUARE-LIST (EQUAL (NTHCDR CUTIL::N (CUTIL::SLOW-SQUARE-LIST CUTIL::X)) (CUTIL::SLOW-SQUARE-LIST (NTHCDR CUTIL::N CUTIL::X))) :HINTS (("Goal" :INDUCT (NTHCDR CUTIL::N CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (NTHCDR CUTIL::SLOW-SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SLOW-SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MEMBER-EQUAL-OF-SQUARE-IN-SLOW-SQUARE-LIST-WHEN-MEMBER-EQUAL (IMPLIES (MEMBER-EQUAL CUTIL::A (DOUBLE-REWRITE CUTIL::X)) (MEMBER-EQUAL (CUTIL::SQUARE CUTIL::A) (CUTIL::SLOW-SQUARE-LIST CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (MEMBER-EQUAL CUTIL::SLOW-SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SLOW-SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SUBSETP-EQUAL-OF-SLOW-SQUARE-LISTS-WHEN-SUBSETP-EQUAL (IMPLIES (SUBSETP-EQUAL (DOUBLE-REWRITE CUTIL::X) (DOUBLE-REWRITE CUTIL::Y)) (SUBSETP-EQUAL (CUTIL::SLOW-SQUARE-LIST CUTIL::X) (CUTIL::SLOW-SQUARE-LIST CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (SUBSETP-EQUAL CUTIL::MEMBER-EQUAL-OF-SQUARE-IN-SLOW-SQUARE-LIST-WHEN-MEMBER-EQUAL CUTIL::SLOW-SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SLOW-SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SLOW-SQUARE-LIST-EXEC-REMOVAL (EQUAL (CUTIL::SLOW-SQUARE-LIST-EXEC CUTIL::X CUTIL::ACC) (REVAPPEND (CUTIL::SLOW-SQUARE-LIST CUTIL::X) CUTIL::ACC)) :HINTS (("Goal" :INDUCT (CUTIL::SLOW-SQUARE-LIST-EXEC CUTIL::X CUTIL::ACC) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SLOW-SQUARE-LIST-EXEC CUTIL::SLOW-SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SLOW-SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (VERIFY-GUARDS CUTIL::SLOW-SQUARE-LIST-EXEC :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SLOW-SQUARE-LIST-EXEC)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (VERIFY-GUARDS CUTIL::SLOW-SQUARE-LIST :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SLOW-SQUARE-LIST CUTIL::SLOW-SQUARE-LIST-EXEC-REMOVAL CUTIL::TRUE-LISTP-OF-SLOW-SQUARE-LIST REVERSE-REMOVAL REVAPPEND-REMOVAL REV-OF-APPEND REV-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (LOCAL (IN-THEORY (ENABLE CUTIL::SLOW-SQUARE-LIST CUTIL::SLOW-SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SLOW-SQUARE-LIST-OF-CONS))))) (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (LOGIC) (DEFUND CUTIL::SLOW-SQUARE-LIST-EXEC (CUTIL::X CUTIL::ACC) (DECLARE (XARGS :GUARD (INTEGER-LISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (IF (CONSP CUTIL::X) (CUTIL::SLOW-SQUARE-LIST-EXEC (CDR CUTIL::X) (CONS (CUTIL::SQUARE (CAR CUTIL::X)) CUTIL::ACC)) CUTIL::ACC)) (DEFUND CUTIL::SLOW-SQUARE-LIST (CUTIL::X) (DECLARE (XARGS :GUARD (INTEGER-LISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (MBE :LOGIC (IF (CONSP CUTIL::X) (CONS (CUTIL::SQUARE (CAR CUTIL::X)) (CUTIL::SLOW-SQUARE-LIST (CDR CUTIL::X))) NIL) :EXEC (REVERSE (CUTIL::SLOW-SQUARE-LIST-EXEC CUTIL::X NIL)))) (SET-INHIBIT-WARNINGS "disable") (RECORD-EXPANSION (LOCAL (MAKE-EVENT (IF (CUTIL::IS-THEOREM-P (QUOTE CUTIL::SLOW-SQUARE-LIST-NIL-PRESERVINGP-LEMMA) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (DEFTHM CUTIL::SLOW-SQUARE-LIST-NIL-PRESERVINGP-LEMMA (OR (EQUAL (ALISTP CUTIL::X) T) (EQUAL (ALISTP CUTIL::X) NIL)) :RULE-CLASSES :TYPE-PRESCRIPTION :HINTS (("Goal" :IN-THEORY (QUOTE ((:TYPE-PRESCRIPTION ALISTP))))))))))) (LOCAL (VALUE-TRIPLE :ELIDED))) (DEFTHM CUTIL::SLOW-SQUARE-LIST-WHEN-NOT-CONSP (IMPLIES (NOT (CONSP CUTIL::X)) (EQUAL (CUTIL::SLOW-SQUARE-LIST CUTIL::X) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SLOW-SQUARE-LIST)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SLOW-SQUARE-LIST-OF-CONS (EQUAL (CUTIL::SLOW-SQUARE-LIST (CONS CUTIL::A CUTIL::X)) (CONS (CUTIL::SQUARE CUTIL::A) (CUTIL::SLOW-SQUARE-LIST CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SLOW-SQUARE-LIST)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::TRUE-LISTP-OF-SLOW-SQUARE-LIST (EQUAL (TRUE-LISTP (CUTIL::SLOW-SQUARE-LIST CUTIL::X)) T) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SLOW-SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SLOW-SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::LEN-OF-SLOW-SQUARE-LIST (EQUAL (LEN (CUTIL::SLOW-SQUARE-LIST CUTIL::X)) (LEN CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SLOW-SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SLOW-SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CONSP-OF-SLOW-SQUARE-LIST (EQUAL (CONSP (CUTIL::SLOW-SQUARE-LIST CUTIL::X)) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SLOW-SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SLOW-SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CAR-OF-SLOW-SQUARE-LIST (EQUAL (CAR (CUTIL::SLOW-SQUARE-LIST CUTIL::X)) (IF (CONSP CUTIL::X) (CUTIL::SQUARE (CAR CUTIL::X)) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SLOW-SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SLOW-SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CDR-OF-SLOW-SQUARE-LIST (EQUAL (CDR (CUTIL::SLOW-SQUARE-LIST CUTIL::X)) (CUTIL::SLOW-SQUARE-LIST (CDR CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SLOW-SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SLOW-SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SLOW-SQUARE-LIST-UNDER-IFF (IFF (CUTIL::SLOW-SQUARE-LIST CUTIL::X) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SLOW-SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SLOW-SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SLOW-SQUARE-LIST-OF-LIST-FIX (EQUAL (CUTIL::SLOW-SQUARE-LIST (LIST-FIX CUTIL::X)) (CUTIL::SLOW-SQUARE-LIST CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SLOW-SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SLOW-SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SLOW-SQUARE-LIST-OF-APPEND (EQUAL (CUTIL::SLOW-SQUARE-LIST (APPEND CUTIL::X CUTIL::Y)) (APPEND (CUTIL::SLOW-SQUARE-LIST CUTIL::X) (CUTIL::SLOW-SQUARE-LIST CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SLOW-SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SLOW-SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SLOW-SQUARE-LIST-OF-REV (EQUAL (CUTIL::SLOW-SQUARE-LIST (REV CUTIL::X)) (REV (CUTIL::SLOW-SQUARE-LIST CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SLOW-SQUARE-LIST-OF-APPEND CUTIL::SLOW-SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SLOW-SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SLOW-SQUARE-LIST-OF-REVAPPEND (EQUAL (CUTIL::SLOW-SQUARE-LIST (REVAPPEND CUTIL::X CUTIL::Y)) (REVAPPEND (CUTIL::SLOW-SQUARE-LIST CUTIL::X) (CUTIL::SLOW-SQUARE-LIST CUTIL::Y))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SLOW-SQUARE-LIST-OF-APPEND CUTIL::SLOW-SQUARE-LIST-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::NTHCDR-OF-SLOW-SQUARE-LIST (EQUAL (NTHCDR CUTIL::N (CUTIL::SLOW-SQUARE-LIST CUTIL::X)) (CUTIL::SLOW-SQUARE-LIST (NTHCDR CUTIL::N CUTIL::X))) :HINTS (("Goal" :INDUCT (NTHCDR CUTIL::N CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (NTHCDR CUTIL::SLOW-SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SLOW-SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MEMBER-EQUAL-OF-SQUARE-IN-SLOW-SQUARE-LIST-WHEN-MEMBER-EQUAL (IMPLIES (MEMBER-EQUAL CUTIL::A (DOUBLE-REWRITE CUTIL::X)) (MEMBER-EQUAL (CUTIL::SQUARE CUTIL::A) (CUTIL::SLOW-SQUARE-LIST CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (MEMBER-EQUAL CUTIL::SLOW-SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SLOW-SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SUBSETP-EQUAL-OF-SLOW-SQUARE-LISTS-WHEN-SUBSETP-EQUAL (IMPLIES (SUBSETP-EQUAL (DOUBLE-REWRITE CUTIL::X) (DOUBLE-REWRITE CUTIL::Y)) (SUBSETP-EQUAL (CUTIL::SLOW-SQUARE-LIST CUTIL::X) (CUTIL::SLOW-SQUARE-LIST CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (SUBSETP-EQUAL CUTIL::MEMBER-EQUAL-OF-SQUARE-IN-SLOW-SQUARE-LIST-WHEN-MEMBER-EQUAL CUTIL::SLOW-SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SLOW-SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SLOW-SQUARE-LIST-EXEC-REMOVAL (EQUAL (CUTIL::SLOW-SQUARE-LIST-EXEC CUTIL::X CUTIL::ACC) (REVAPPEND (CUTIL::SLOW-SQUARE-LIST CUTIL::X) CUTIL::ACC)) :HINTS (("Goal" :INDUCT (CUTIL::SLOW-SQUARE-LIST-EXEC CUTIL::X CUTIL::ACC) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SLOW-SQUARE-LIST-EXEC CUTIL::SLOW-SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SLOW-SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (VERIFY-GUARDS CUTIL::SLOW-SQUARE-LIST-EXEC :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SLOW-SQUARE-LIST-EXEC)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (VERIFY-GUARDS CUTIL::SLOW-SQUARE-LIST :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SLOW-SQUARE-LIST CUTIL::SLOW-SQUARE-LIST-EXEC-REMOVAL CUTIL::TRUE-LISTP-OF-SLOW-SQUARE-LIST REVERSE-REMOVAL REVAPPEND-REMOVAL REV-OF-APPEND REV-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (LOCAL (IN-THEORY (ENABLE CUTIL::SLOW-SQUARE-LIST CUTIL::SLOW-SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SLOW-SQUARE-LIST-OF-CONS)))))) (RECORD-EXPANSION (MAKE-EVENT (LET* ((XDOC::NAME (QUOTE CUTIL::SLOW-SQUARE-LIST)) (XDOC::PARENTS (QUOTE (UNDOCUMENTED))) (XDOC::SHORT (QUOTE "@(call SLOW-SQUARE-LIST) maps @(see CUTIL::SQUARE) across a list.")) (XDOC::EXTENSION (QUOTE NIL)) (XDOC::WRLD (W STATE)) (XDOC::TRIPS (REVERSED-WORLD-SINCE-EVENT XDOC::WRLD (QUOTE (TABLE INTRO-TABLE :MARK (QUOTE CUTIL::SLOW-SQUARE-LIST))) NIL)) (XDOC::INFO (REVERSE (NEW-FORMULA-INFO XDOC::TRIPS XDOC::WRLD NIL))) (XDOC::AUTODOC (XDOC::FORMULA-INFO-TO-DEFS (NOT XDOC::EXTENSION) XDOC::INFO)) (XDOC::LONG (CONCATENATE (QUOTE STRING) (QUOTE "<p>This is an ordinary @(see defprojection).</p>") (COERCE (LIST #\Newline #\Newline) (QUOTE STRING)) XDOC::AUTODOC))) (IF XDOC::EXTENSION (CONS (QUOTE XDOC-EXTEND) (CONS XDOC::EXTENSION (CONS XDOC::LONG (QUOTE NIL)))) (CONS (QUOTE DEFXDOC) (CONS XDOC::NAME (CONS (QUOTE :PARENTS) (CONS XDOC::PARENTS (CONS (QUOTE :SHORT) (CONS XDOC::SHORT (CONS (QUOTE :LONG) (CONS XDOC::LONG (QUOTE NIL)))))))))))) (WITH-OUTPUT :OFF (EVENT SUMMARY) (PROGN (TABLE XDOC (QUOTE DOC) (CONS (QUOTE ((:NAME . CUTIL::SLOW-SQUARE-LIST) (:BASE-PKG . CUTIL::ACL2-PKG-WITNESS) (:PARENTS UNDOCUMENTED) (:SHORT . "@(call SLOW-SQUARE-LIST) maps @(see CUTIL::SQUARE) across a list.") (:LONG . "<p>This is an ordinary @(see defprojection).</p>

<h3>Definitions and Theorems</h3>@(def |CUTIL|::|SLOW-SQUARE-LIST-EXEC|)
@(def |CUTIL|::|SLOW-SQUARE-LIST|)
@(def |CUTIL|::|SLOW-SQUARE-LIST-WHEN-NOT-CONSP|)
@(def |CUTIL|::|SLOW-SQUARE-LIST-OF-CONS|)
@(def |CUTIL|::|TRUE-LISTP-OF-SLOW-SQUARE-LIST|)
@(def |CUTIL|::|LEN-OF-SLOW-SQUARE-LIST|)
@(def |CUTIL|::|CONSP-OF-SLOW-SQUARE-LIST|)
@(def |CUTIL|::|CAR-OF-SLOW-SQUARE-LIST|)
@(def |CUTIL|::|CDR-OF-SLOW-SQUARE-LIST|)
@(def |CUTIL|::|SLOW-SQUARE-LIST-UNDER-IFF|)
@(def |CUTIL|::|SLOW-SQUARE-LIST-OF-LIST-FIX|)
@(def |CUTIL|::|SLOW-SQUARE-LIST-OF-APPEND|)
@(def |CUTIL|::|SLOW-SQUARE-LIST-OF-REV|)
@(def |CUTIL|::|SLOW-SQUARE-LIST-OF-REVAPPEND|)
@(def |CUTIL|::|NTHCDR-OF-SLOW-SQUARE-LIST|)
@(def |CUTIL|::|MEMBER-EQUAL-OF-SQUARE-IN-SLOW-SQUARE-LIST-WHEN-MEMBER-EQUAL|)
@(def |CUTIL|::|SUBSETP-EQUAL-OF-SLOW-SQUARE-LISTS-WHEN-SUBSETP-EQUAL|)
@(def |CUTIL|::|SLOW-SQUARE-LIST-EXEC-REMOVAL|)") (:FROM . "[books]/cutil/defprojection-tests.lisp"))) (XDOC::GET-XDOC-TABLE WORLD))) (VALUE-TRIPLE (QUOTE (DEFXDOC CUTIL::SLOW-SQUARE-LIST)))))) (VALUE-TRIPLE (QUOTE CUTIL::SLOW-SQUARE-LIST))))) (13 RECORD-EXPANSION (CUTIL::DEFPROJECTION CUTIL::SQUARE-LIST (CUTIL::X) (CUTIL::SQUARE CUTIL::X) :GUARD (INTEGER-LISTP CUTIL::X)) (WITH-OUTPUT :STACK :PUSH :OFF :ALL :ON ERROR (PROGN (TABLE INTRO-TABLE :MARK (QUOTE CUTIL::SQUARE-LIST)) (RECORD-EXPANSION (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (LOGIC) (DEFUND CUTIL::SQUARE-LIST-EXEC (CUTIL::X CUTIL::ACC) (DECLARE (XARGS :GUARD (INTEGER-LISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (IF (CONSP CUTIL::X) (CUTIL::SQUARE-LIST-EXEC (CDR CUTIL::X) (CONS (CUTIL::SQUARE (CAR CUTIL::X)) CUTIL::ACC)) CUTIL::ACC)) (DEFUND CUTIL::SQUARE-LIST (CUTIL::X) (DECLARE (XARGS :GUARD (INTEGER-LISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (MBE :LOGIC (IF (CONSP CUTIL::X) (CONS (CUTIL::SQUARE (CAR CUTIL::X)) (CUTIL::SQUARE-LIST (CDR CUTIL::X))) NIL) :EXEC (REVERSE (CUTIL::SQUARE-LIST-EXEC CUTIL::X NIL)))) (SET-INHIBIT-WARNINGS "disable") (LOCAL (MAKE-EVENT (IF (CUTIL::IS-THEOREM-P (QUOTE CUTIL::SQUARE-LIST-NIL-PRESERVINGP-LEMMA) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (DEFTHM CUTIL::SQUARE-LIST-NIL-PRESERVINGP-LEMMA (OR (EQUAL (ALISTP CUTIL::X) T) (EQUAL (ALISTP CUTIL::X) NIL)) :RULE-CLASSES :TYPE-PRESCRIPTION :HINTS (("Goal" :IN-THEORY (QUOTE ((:TYPE-PRESCRIPTION ALISTP))))))))))) (DEFTHM CUTIL::SQUARE-LIST-WHEN-NOT-CONSP (IMPLIES (NOT (CONSP CUTIL::X)) (EQUAL (CUTIL::SQUARE-LIST CUTIL::X) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-OF-CONS (EQUAL (CUTIL::SQUARE-LIST (CONS CUTIL::A CUTIL::X)) (CONS (CUTIL::SQUARE CUTIL::A) (CUTIL::SQUARE-LIST CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::TRUE-LISTP-OF-SQUARE-LIST (EQUAL (TRUE-LISTP (CUTIL::SQUARE-LIST CUTIL::X)) T) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::LEN-OF-SQUARE-LIST (EQUAL (LEN (CUTIL::SQUARE-LIST CUTIL::X)) (LEN CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CONSP-OF-SQUARE-LIST (EQUAL (CONSP (CUTIL::SQUARE-LIST CUTIL::X)) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CAR-OF-SQUARE-LIST (EQUAL (CAR (CUTIL::SQUARE-LIST CUTIL::X)) (IF (CONSP CUTIL::X) (CUTIL::SQUARE (CAR CUTIL::X)) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CDR-OF-SQUARE-LIST (EQUAL (CDR (CUTIL::SQUARE-LIST CUTIL::X)) (CUTIL::SQUARE-LIST (CDR CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-UNDER-IFF (IFF (CUTIL::SQUARE-LIST CUTIL::X) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-OF-LIST-FIX (EQUAL (CUTIL::SQUARE-LIST (LIST-FIX CUTIL::X)) (CUTIL::SQUARE-LIST CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-OF-APPEND (EQUAL (CUTIL::SQUARE-LIST (APPEND CUTIL::X CUTIL::Y)) (APPEND (CUTIL::SQUARE-LIST CUTIL::X) (CUTIL::SQUARE-LIST CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-OF-REV (EQUAL (CUTIL::SQUARE-LIST (REV CUTIL::X)) (REV (CUTIL::SQUARE-LIST CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-OF-APPEND CUTIL::SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-OF-REVAPPEND (EQUAL (CUTIL::SQUARE-LIST (REVAPPEND CUTIL::X CUTIL::Y)) (REVAPPEND (CUTIL::SQUARE-LIST CUTIL::X) (CUTIL::SQUARE-LIST CUTIL::Y))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-OF-APPEND CUTIL::SQUARE-LIST-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::NTHCDR-OF-SQUARE-LIST (EQUAL (NTHCDR CUTIL::N (CUTIL::SQUARE-LIST CUTIL::X)) (CUTIL::SQUARE-LIST (NTHCDR CUTIL::N CUTIL::X))) :HINTS (("Goal" :INDUCT (NTHCDR CUTIL::N CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (NTHCDR CUTIL::SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MEMBER-EQUAL-OF-SQUARE-IN-SQUARE-LIST-WHEN-MEMBER-EQUAL (IMPLIES (MEMBER-EQUAL CUTIL::A (DOUBLE-REWRITE CUTIL::X)) (MEMBER-EQUAL (CUTIL::SQUARE CUTIL::A) (CUTIL::SQUARE-LIST CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (MEMBER-EQUAL CUTIL::SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SUBSETP-EQUAL-OF-SQUARE-LISTS-WHEN-SUBSETP-EQUAL (IMPLIES (SUBSETP-EQUAL (DOUBLE-REWRITE CUTIL::X) (DOUBLE-REWRITE CUTIL::Y)) (SUBSETP-EQUAL (CUTIL::SQUARE-LIST CUTIL::X) (CUTIL::SQUARE-LIST CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (SUBSETP-EQUAL CUTIL::MEMBER-EQUAL-OF-SQUARE-IN-SQUARE-LIST-WHEN-MEMBER-EQUAL CUTIL::SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-EXEC-REMOVAL (EQUAL (CUTIL::SQUARE-LIST-EXEC CUTIL::X CUTIL::ACC) (REVAPPEND (CUTIL::SQUARE-LIST CUTIL::X) CUTIL::ACC)) :HINTS (("Goal" :INDUCT (CUTIL::SQUARE-LIST-EXEC CUTIL::X CUTIL::ACC) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-EXEC CUTIL::SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (VERIFY-GUARDS CUTIL::SQUARE-LIST-EXEC :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-EXEC)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (VERIFY-GUARDS CUTIL::SQUARE-LIST :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST CUTIL::SQUARE-LIST-EXEC-REMOVAL CUTIL::TRUE-LISTP-OF-SQUARE-LIST REVERSE-REMOVAL REVAPPEND-REMOVAL REV-OF-APPEND REV-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (PROGN (MAKE-EVENT (IF (GLOBAL-VAL (QUOTE INCLUDE-BOOK-PATH) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::SQUARE-LIST) (QUOTE (DEFUN CUTIL::SQUARE-LIST (CUTIL::X) (NREVERSE (CUTIL::SQUARE-LIST-EXEC CUTIL::X NIL)))))))))) (DEFTTAG CUTIL::CUTIL-OPTIMIZE) (NEVER-MEMOIZE CUTIL::SQUARE-LIST-EXEC) (PROGN! (SET-RAW-MODE T) (DEFUN CUTIL::SQUARE-LIST (CUTIL::X) (NREVERSE (CUTIL::SQUARE-LIST-EXEC CUTIL::X NIL)))) (DEFTTAG NIL)) (LOCAL (IN-THEORY (ENABLE CUTIL::SQUARE-LIST CUTIL::SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-OF-CONS))))) (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (LOGIC) (DEFUND CUTIL::SQUARE-LIST-EXEC (CUTIL::X CUTIL::ACC) (DECLARE (XARGS :GUARD (INTEGER-LISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (IF (CONSP CUTIL::X) (CUTIL::SQUARE-LIST-EXEC (CDR CUTIL::X) (CONS (CUTIL::SQUARE (CAR CUTIL::X)) CUTIL::ACC)) CUTIL::ACC)) (DEFUND CUTIL::SQUARE-LIST (CUTIL::X) (DECLARE (XARGS :GUARD (INTEGER-LISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (MBE :LOGIC (IF (CONSP CUTIL::X) (CONS (CUTIL::SQUARE (CAR CUTIL::X)) (CUTIL::SQUARE-LIST (CDR CUTIL::X))) NIL) :EXEC (REVERSE (CUTIL::SQUARE-LIST-EXEC CUTIL::X NIL)))) (SET-INHIBIT-WARNINGS "disable") (RECORD-EXPANSION (LOCAL (MAKE-EVENT (IF (CUTIL::IS-THEOREM-P (QUOTE CUTIL::SQUARE-LIST-NIL-PRESERVINGP-LEMMA) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (DEFTHM CUTIL::SQUARE-LIST-NIL-PRESERVINGP-LEMMA (OR (EQUAL (ALISTP CUTIL::X) T) (EQUAL (ALISTP CUTIL::X) NIL)) :RULE-CLASSES :TYPE-PRESCRIPTION :HINTS (("Goal" :IN-THEORY (QUOTE ((:TYPE-PRESCRIPTION ALISTP))))))))))) (LOCAL (VALUE-TRIPLE :ELIDED))) (DEFTHM CUTIL::SQUARE-LIST-WHEN-NOT-CONSP (IMPLIES (NOT (CONSP CUTIL::X)) (EQUAL (CUTIL::SQUARE-LIST CUTIL::X) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-OF-CONS (EQUAL (CUTIL::SQUARE-LIST (CONS CUTIL::A CUTIL::X)) (CONS (CUTIL::SQUARE CUTIL::A) (CUTIL::SQUARE-LIST CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::TRUE-LISTP-OF-SQUARE-LIST (EQUAL (TRUE-LISTP (CUTIL::SQUARE-LIST CUTIL::X)) T) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::LEN-OF-SQUARE-LIST (EQUAL (LEN (CUTIL::SQUARE-LIST CUTIL::X)) (LEN CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CONSP-OF-SQUARE-LIST (EQUAL (CONSP (CUTIL::SQUARE-LIST CUTIL::X)) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CAR-OF-SQUARE-LIST (EQUAL (CAR (CUTIL::SQUARE-LIST CUTIL::X)) (IF (CONSP CUTIL::X) (CUTIL::SQUARE (CAR CUTIL::X)) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CDR-OF-SQUARE-LIST (EQUAL (CDR (CUTIL::SQUARE-LIST CUTIL::X)) (CUTIL::SQUARE-LIST (CDR CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-UNDER-IFF (IFF (CUTIL::SQUARE-LIST CUTIL::X) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-OF-LIST-FIX (EQUAL (CUTIL::SQUARE-LIST (LIST-FIX CUTIL::X)) (CUTIL::SQUARE-LIST CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-OF-APPEND (EQUAL (CUTIL::SQUARE-LIST (APPEND CUTIL::X CUTIL::Y)) (APPEND (CUTIL::SQUARE-LIST CUTIL::X) (CUTIL::SQUARE-LIST CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-OF-REV (EQUAL (CUTIL::SQUARE-LIST (REV CUTIL::X)) (REV (CUTIL::SQUARE-LIST CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-OF-APPEND CUTIL::SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-OF-REVAPPEND (EQUAL (CUTIL::SQUARE-LIST (REVAPPEND CUTIL::X CUTIL::Y)) (REVAPPEND (CUTIL::SQUARE-LIST CUTIL::X) (CUTIL::SQUARE-LIST CUTIL::Y))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-OF-APPEND CUTIL::SQUARE-LIST-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::NTHCDR-OF-SQUARE-LIST (EQUAL (NTHCDR CUTIL::N (CUTIL::SQUARE-LIST CUTIL::X)) (CUTIL::SQUARE-LIST (NTHCDR CUTIL::N CUTIL::X))) :HINTS (("Goal" :INDUCT (NTHCDR CUTIL::N CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (NTHCDR CUTIL::SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MEMBER-EQUAL-OF-SQUARE-IN-SQUARE-LIST-WHEN-MEMBER-EQUAL (IMPLIES (MEMBER-EQUAL CUTIL::A (DOUBLE-REWRITE CUTIL::X)) (MEMBER-EQUAL (CUTIL::SQUARE CUTIL::A) (CUTIL::SQUARE-LIST CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (MEMBER-EQUAL CUTIL::SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SUBSETP-EQUAL-OF-SQUARE-LISTS-WHEN-SUBSETP-EQUAL (IMPLIES (SUBSETP-EQUAL (DOUBLE-REWRITE CUTIL::X) (DOUBLE-REWRITE CUTIL::Y)) (SUBSETP-EQUAL (CUTIL::SQUARE-LIST CUTIL::X) (CUTIL::SQUARE-LIST CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (SUBSETP-EQUAL CUTIL::MEMBER-EQUAL-OF-SQUARE-IN-SQUARE-LIST-WHEN-MEMBER-EQUAL CUTIL::SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-EXEC-REMOVAL (EQUAL (CUTIL::SQUARE-LIST-EXEC CUTIL::X CUTIL::ACC) (REVAPPEND (CUTIL::SQUARE-LIST CUTIL::X) CUTIL::ACC)) :HINTS (("Goal" :INDUCT (CUTIL::SQUARE-LIST-EXEC CUTIL::X CUTIL::ACC) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-EXEC CUTIL::SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (VERIFY-GUARDS CUTIL::SQUARE-LIST-EXEC :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-EXEC)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (VERIFY-GUARDS CUTIL::SQUARE-LIST :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST CUTIL::SQUARE-LIST-EXEC-REMOVAL CUTIL::TRUE-LISTP-OF-SQUARE-LIST REVERSE-REMOVAL REVAPPEND-REMOVAL REV-OF-APPEND REV-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (RECORD-EXPANSION (PROGN (MAKE-EVENT (IF (GLOBAL-VAL (QUOTE INCLUDE-BOOK-PATH) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::SQUARE-LIST) (QUOTE (DEFUN CUTIL::SQUARE-LIST (CUTIL::X) (NREVERSE (CUTIL::SQUARE-LIST-EXEC CUTIL::X NIL)))))))))) (DEFTTAG CUTIL::CUTIL-OPTIMIZE) (NEVER-MEMOIZE CUTIL::SQUARE-LIST-EXEC) (PROGN! (SET-RAW-MODE T) (DEFUN CUTIL::SQUARE-LIST (CUTIL::X) (NREVERSE (CUTIL::SQUARE-LIST-EXEC CUTIL::X NIL)))) (DEFTTAG NIL)) (PROGN (RECORD-EXPANSION (MAKE-EVENT (IF (GLOBAL-VAL (QUOTE INCLUDE-BOOK-PATH) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::SQUARE-LIST) (QUOTE (DEFUN CUTIL::SQUARE-LIST (CUTIL::X) (NREVERSE (CUTIL::SQUARE-LIST-EXEC CUTIL::X NIL)))))))))) (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::SQUARE-LIST) (QUOTE (DEFUN CUTIL::SQUARE-LIST (CUTIL::X) (NREVERSE (CUTIL::SQUARE-LIST-EXEC CUTIL::X NIL))))))) (DEFTTAG CUTIL::CUTIL-OPTIMIZE) (RECORD-EXPANSION (NEVER-MEMOIZE CUTIL::SQUARE-LIST-EXEC) (MAKE-EVENT (PROG2$ (NEVER-MEMOIZE-FN (QUOTE CUTIL::SQUARE-LIST-EXEC)) (QUOTE (VALUE-TRIPLE :INVISIBLE))) :CHECK-EXPANSION (VALUE-TRIPLE :INVISIBLE))) (PROGN! (SET-RAW-MODE T) (DEFUN CUTIL::SQUARE-LIST (CUTIL::X) (NREVERSE (CUTIL::SQUARE-LIST-EXEC CUTIL::X NIL)))) (DEFTTAG NIL))) (LOCAL (IN-THEORY (ENABLE CUTIL::SQUARE-LIST CUTIL::SQUARE-LIST-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-OF-CONS)))))) (RECORD-EXPANSION (MAKE-EVENT (LET* ((XDOC::NAME (QUOTE CUTIL::SQUARE-LIST)) (XDOC::PARENTS (QUOTE (UNDOCUMENTED))) (XDOC::SHORT (QUOTE "@(call SQUARE-LIST) maps @(see CUTIL::SQUARE) across a list.")) (XDOC::EXTENSION (QUOTE NIL)) (XDOC::WRLD (W STATE)) (XDOC::TRIPS (REVERSED-WORLD-SINCE-EVENT XDOC::WRLD (QUOTE (TABLE INTRO-TABLE :MARK (QUOTE CUTIL::SQUARE-LIST))) NIL)) (XDOC::INFO (REVERSE (NEW-FORMULA-INFO XDOC::TRIPS XDOC::WRLD NIL))) (XDOC::AUTODOC (XDOC::FORMULA-INFO-TO-DEFS (NOT XDOC::EXTENSION) XDOC::INFO)) (XDOC::LONG (CONCATENATE (QUOTE STRING) (QUOTE "<p>This is an ordinary @(see defprojection).</p>") (COERCE (LIST #\Newline #\Newline) (QUOTE STRING)) XDOC::AUTODOC))) (IF XDOC::EXTENSION (CONS (QUOTE XDOC-EXTEND) (CONS XDOC::EXTENSION (CONS XDOC::LONG (QUOTE NIL)))) (CONS (QUOTE DEFXDOC) (CONS XDOC::NAME (CONS (QUOTE :PARENTS) (CONS XDOC::PARENTS (CONS (QUOTE :SHORT) (CONS XDOC::SHORT (CONS (QUOTE :LONG) (CONS XDOC::LONG (QUOTE NIL)))))))))))) (WITH-OUTPUT :OFF (EVENT SUMMARY) (PROGN (TABLE XDOC (QUOTE DOC) (CONS (QUOTE ((:NAME . CUTIL::SQUARE-LIST) (:BASE-PKG . CUTIL::ACL2-PKG-WITNESS) (:PARENTS UNDOCUMENTED) (:SHORT . "@(call SQUARE-LIST) maps @(see CUTIL::SQUARE) across a list.") (:LONG . "<p>This is an ordinary @(see defprojection).</p>

<h3>Definitions and Theorems</h3>@(def |CUTIL|::|SQUARE-LIST-EXEC|)
@(def |CUTIL|::|SQUARE-LIST|)
@(def |CUTIL|::|SQUARE-LIST-WHEN-NOT-CONSP|)
@(def |CUTIL|::|SQUARE-LIST-OF-CONS|)
@(def |CUTIL|::|TRUE-LISTP-OF-SQUARE-LIST|)
@(def |CUTIL|::|LEN-OF-SQUARE-LIST|)
@(def |CUTIL|::|CONSP-OF-SQUARE-LIST|)
@(def |CUTIL|::|CAR-OF-SQUARE-LIST|)
@(def |CUTIL|::|CDR-OF-SQUARE-LIST|)
@(def |CUTIL|::|SQUARE-LIST-UNDER-IFF|)
@(def |CUTIL|::|SQUARE-LIST-OF-LIST-FIX|)
@(def |CUTIL|::|SQUARE-LIST-OF-APPEND|)
@(def |CUTIL|::|SQUARE-LIST-OF-REV|)
@(def |CUTIL|::|SQUARE-LIST-OF-REVAPPEND|)
@(def |CUTIL|::|NTHCDR-OF-SQUARE-LIST|)
@(def |CUTIL|::|MEMBER-EQUAL-OF-SQUARE-IN-SQUARE-LIST-WHEN-MEMBER-EQUAL|)
@(def |CUTIL|::|SUBSETP-EQUAL-OF-SQUARE-LISTS-WHEN-SUBSETP-EQUAL|)
@(def |CUTIL|::|SQUARE-LIST-EXEC-REMOVAL|)") (:FROM . "[books]/cutil/defprojection-tests.lisp"))) (XDOC::GET-XDOC-TABLE WORLD))) (VALUE-TRIPLE (QUOTE (DEFXDOC CUTIL::SQUARE-LIST)))))) (VALUE-TRIPLE (QUOTE CUTIL::SQUARE-LIST))))) (14 RECORD-EXPANSION (CUTIL::DEFPROJECTION CUTIL::PROGRAM-SQUARE-LIST (CUTIL::X) (CUTIL::SQUARE CUTIL::X) :GUARD (INTEGER-LISTP CUTIL::X) :MODE :PROGRAM) (WITH-OUTPUT :STACK :PUSH :OFF :ALL :ON ERROR (PROGN (TABLE INTRO-TABLE :MARK (QUOTE CUTIL::PROGRAM-SQUARE-LIST)) (RECORD-EXPANSION (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (PROGRAM) (DEFUND CUTIL::PROGRAM-SQUARE-LIST-EXEC (CUTIL::X CUTIL::ACC) (DECLARE (XARGS :GUARD (INTEGER-LISTP CUTIL::X) :MODE :PROGRAM :NORMALIZE NIL :VERIFY-GUARDS NIL)) (IF (CONSP CUTIL::X) (CUTIL::PROGRAM-SQUARE-LIST-EXEC (CDR CUTIL::X) (CONS (CUTIL::SQUARE (CAR CUTIL::X)) CUTIL::ACC)) CUTIL::ACC)) (DEFUND CUTIL::PROGRAM-SQUARE-LIST (CUTIL::X) (DECLARE (XARGS :GUARD (INTEGER-LISTP CUTIL::X) :MODE :PROGRAM :NORMALIZE NIL :VERIFY-GUARDS NIL)) (MBE :LOGIC (IF (CONSP CUTIL::X) (CONS (CUTIL::SQUARE (CAR CUTIL::X)) (CUTIL::PROGRAM-SQUARE-LIST (CDR CUTIL::X))) NIL) :EXEC (REVERSE (CUTIL::PROGRAM-SQUARE-LIST-EXEC CUTIL::X NIL)))) (PROGN (MAKE-EVENT (IF (GLOBAL-VAL (QUOTE INCLUDE-BOOK-PATH) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::PROGRAM-SQUARE-LIST) (QUOTE (DEFUN CUTIL::PROGRAM-SQUARE-LIST (CUTIL::X) (NREVERSE (CUTIL::PROGRAM-SQUARE-LIST-EXEC CUTIL::X NIL)))))))))) (DEFTTAG CUTIL::CUTIL-OPTIMIZE) (NEVER-MEMOIZE CUTIL::PROGRAM-SQUARE-LIST-EXEC) (PROGN! (SET-RAW-MODE T) (DEFUN CUTIL::PROGRAM-SQUARE-LIST (CUTIL::X) (NREVERSE (CUTIL::PROGRAM-SQUARE-LIST-EXEC CUTIL::X NIL)))) (DEFTTAG NIL)))) (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (PROGRAM) (DEFUND CUTIL::PROGRAM-SQUARE-LIST-EXEC (CUTIL::X CUTIL::ACC) (DECLARE (XARGS :GUARD (INTEGER-LISTP CUTIL::X) :MODE :PROGRAM :NORMALIZE NIL :VERIFY-GUARDS NIL)) (IF (CONSP CUTIL::X) (CUTIL::PROGRAM-SQUARE-LIST-EXEC (CDR CUTIL::X) (CONS (CUTIL::SQUARE (CAR CUTIL::X)) CUTIL::ACC)) CUTIL::ACC)) (DEFUND CUTIL::PROGRAM-SQUARE-LIST (CUTIL::X) (DECLARE (XARGS :GUARD (INTEGER-LISTP CUTIL::X) :MODE :PROGRAM :NORMALIZE NIL :VERIFY-GUARDS NIL)) (MBE :LOGIC (IF (CONSP CUTIL::X) (CONS (CUTIL::SQUARE (CAR CUTIL::X)) (CUTIL::PROGRAM-SQUARE-LIST (CDR CUTIL::X))) NIL) :EXEC (REVERSE (CUTIL::PROGRAM-SQUARE-LIST-EXEC CUTIL::X NIL)))) (RECORD-EXPANSION (PROGN (MAKE-EVENT (IF (GLOBAL-VAL (QUOTE INCLUDE-BOOK-PATH) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::PROGRAM-SQUARE-LIST) (QUOTE (DEFUN CUTIL::PROGRAM-SQUARE-LIST (CUTIL::X) (NREVERSE (CUTIL::PROGRAM-SQUARE-LIST-EXEC CUTIL::X NIL)))))))))) (DEFTTAG CUTIL::CUTIL-OPTIMIZE) (NEVER-MEMOIZE CUTIL::PROGRAM-SQUARE-LIST-EXEC) (PROGN! (SET-RAW-MODE T) (DEFUN CUTIL::PROGRAM-SQUARE-LIST (CUTIL::X) (NREVERSE (CUTIL::PROGRAM-SQUARE-LIST-EXEC CUTIL::X NIL)))) (DEFTTAG NIL)) (PROGN (RECORD-EXPANSION (MAKE-EVENT (IF (GLOBAL-VAL (QUOTE INCLUDE-BOOK-PATH) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::PROGRAM-SQUARE-LIST) (QUOTE (DEFUN CUTIL::PROGRAM-SQUARE-LIST (CUTIL::X) (NREVERSE (CUTIL::PROGRAM-SQUARE-LIST-EXEC CUTIL::X NIL)))))))))) (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::PROGRAM-SQUARE-LIST) (QUOTE (DEFUN CUTIL::PROGRAM-SQUARE-LIST (CUTIL::X) (NREVERSE (CUTIL::PROGRAM-SQUARE-LIST-EXEC CUTIL::X NIL))))))) (DEFTTAG CUTIL::CUTIL-OPTIMIZE) (RECORD-EXPANSION (NEVER-MEMOIZE CUTIL::PROGRAM-SQUARE-LIST-EXEC) (MAKE-EVENT (PROG2$ (NEVER-MEMOIZE-FN (QUOTE CUTIL::PROGRAM-SQUARE-LIST-EXEC)) (QUOTE (VALUE-TRIPLE :INVISIBLE))) :CHECK-EXPANSION (VALUE-TRIPLE :INVISIBLE))) (PROGN! (SET-RAW-MODE T) (DEFUN CUTIL::PROGRAM-SQUARE-LIST (CUTIL::X) (NREVERSE (CUTIL::PROGRAM-SQUARE-LIST-EXEC CUTIL::X NIL)))) (DEFTTAG NIL)))))) (RECORD-EXPANSION (MAKE-EVENT (LET* ((XDOC::NAME (QUOTE CUTIL::PROGRAM-SQUARE-LIST)) (XDOC::PARENTS (QUOTE (UNDOCUMENTED))) (XDOC::SHORT (QUOTE "@(call PROGRAM-SQUARE-LIST) maps @(see CUTIL::SQUARE) across a list.")) (XDOC::EXTENSION (QUOTE NIL)) (XDOC::WRLD (W STATE)) (XDOC::TRIPS (REVERSED-WORLD-SINCE-EVENT XDOC::WRLD (QUOTE (TABLE INTRO-TABLE :MARK (QUOTE CUTIL::PROGRAM-SQUARE-LIST))) NIL)) (XDOC::INFO (REVERSE (NEW-FORMULA-INFO XDOC::TRIPS XDOC::WRLD NIL))) (XDOC::AUTODOC (XDOC::FORMULA-INFO-TO-DEFS (NOT XDOC::EXTENSION) XDOC::INFO)) (XDOC::LONG (CONCATENATE (QUOTE STRING) (QUOTE "<p>This is an ordinary @(see defprojection).</p>") (COERCE (LIST #\Newline #\Newline) (QUOTE STRING)) XDOC::AUTODOC))) (IF XDOC::EXTENSION (CONS (QUOTE XDOC-EXTEND) (CONS XDOC::EXTENSION (CONS XDOC::LONG (QUOTE NIL)))) (CONS (QUOTE DEFXDOC) (CONS XDOC::NAME (CONS (QUOTE :PARENTS) (CONS XDOC::PARENTS (CONS (QUOTE :SHORT) (CONS XDOC::SHORT (CONS (QUOTE :LONG) (CONS XDOC::LONG (QUOTE NIL)))))))))))) (WITH-OUTPUT :OFF (EVENT SUMMARY) (PROGN (TABLE XDOC (QUOTE DOC) (CONS (QUOTE ((:NAME . CUTIL::PROGRAM-SQUARE-LIST) (:BASE-PKG . CUTIL::ACL2-PKG-WITNESS) (:PARENTS UNDOCUMENTED) (:SHORT . "@(call PROGRAM-SQUARE-LIST) maps @(see CUTIL::SQUARE) across a list.") (:LONG . "<p>This is an ordinary @(see defprojection).</p>

<h3>Definitions and Theorems</h3>@(def |CUTIL|::|PROGRAM-SQUARE-LIST-EXEC|)
@(def |CUTIL|::|PROGRAM-SQUARE-LIST|)") (:FROM . "[books]/cutil/defprojection-tests.lisp"))) (XDOC::GET-XDOC-TABLE WORLD))) (VALUE-TRIPLE (QUOTE (DEFXDOC CUTIL::PROGRAM-SQUARE-LIST)))))) (VALUE-TRIPLE (QUOTE CUTIL::PROGRAM-SQUARE-LIST))))) (15 RECORD-EXPANSION (ASSERT! (LET ((CUTIL::X (QUOTE (1 2 3 4 5 6 7 8 9 10)))) (AND (EQUAL (CUTIL::SQUARE-LIST CUTIL::X) (CUTIL::SLOW-SQUARE-LIST CUTIL::X)) (EQUAL (CUTIL::SQUARE-LIST CUTIL::X) (CUTIL::PROGRAM-SQUARE-LIST CUTIL::X))))) (VALUE-TRIPLE :SUCCESS)) (18 RECORD-EXPANSION (CUTIL::DEFPROJECTION CUTIL::SQUARE-LIST-R (CUTIL::X) (CUTIL::SQUARE CUTIL::X) :GUARD (INTEGER-LISTP CUTIL::X) :RESULT-TYPE INTEGER-LISTP :OPTIMIZE NIL) (WITH-OUTPUT :STACK :PUSH :OFF :ALL :ON ERROR (PROGN (TABLE INTRO-TABLE :MARK (QUOTE CUTIL::SQUARE-LIST-R)) (RECORD-EXPANSION (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (LOGIC) (DEFUND CUTIL::SQUARE-LIST-R-EXEC (CUTIL::X CUTIL::ACC) (DECLARE (XARGS :GUARD (INTEGER-LISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (IF (CONSP CUTIL::X) (CUTIL::SQUARE-LIST-R-EXEC (CDR CUTIL::X) (CONS (CUTIL::SQUARE (CAR CUTIL::X)) CUTIL::ACC)) CUTIL::ACC)) (DEFUND CUTIL::SQUARE-LIST-R (CUTIL::X) (DECLARE (XARGS :GUARD (INTEGER-LISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (MBE :LOGIC (IF (CONSP CUTIL::X) (CONS (CUTIL::SQUARE (CAR CUTIL::X)) (CUTIL::SQUARE-LIST-R (CDR CUTIL::X))) NIL) :EXEC (REVERSE (CUTIL::SQUARE-LIST-R-EXEC CUTIL::X NIL)))) (SET-INHIBIT-WARNINGS "disable") (LOCAL (MAKE-EVENT (IF (CUTIL::IS-THEOREM-P (QUOTE CUTIL::SQUARE-LIST-R-NIL-PRESERVINGP-LEMMA) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (DEFTHM CUTIL::SQUARE-LIST-R-NIL-PRESERVINGP-LEMMA (OR (EQUAL (ALISTP CUTIL::X) T) (EQUAL (ALISTP CUTIL::X) NIL)) :RULE-CLASSES :TYPE-PRESCRIPTION :HINTS (("Goal" :IN-THEORY (QUOTE ((:TYPE-PRESCRIPTION ALISTP))))))))))) (DEFTHM CUTIL::SQUARE-LIST-R-WHEN-NOT-CONSP (IMPLIES (NOT (CONSP CUTIL::X)) (EQUAL (CUTIL::SQUARE-LIST-R CUTIL::X) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-R-OF-CONS (EQUAL (CUTIL::SQUARE-LIST-R (CONS CUTIL::A CUTIL::X)) (CONS (CUTIL::SQUARE CUTIL::A) (CUTIL::SQUARE-LIST-R CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::TRUE-LISTP-OF-SQUARE-LIST-R (EQUAL (TRUE-LISTP (CUTIL::SQUARE-LIST-R CUTIL::X)) T) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::LEN-OF-SQUARE-LIST-R (EQUAL (LEN (CUTIL::SQUARE-LIST-R CUTIL::X)) (LEN CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CONSP-OF-SQUARE-LIST-R (EQUAL (CONSP (CUTIL::SQUARE-LIST-R CUTIL::X)) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CAR-OF-SQUARE-LIST-R (EQUAL (CAR (CUTIL::SQUARE-LIST-R CUTIL::X)) (IF (CONSP CUTIL::X) (CUTIL::SQUARE (CAR CUTIL::X)) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CDR-OF-SQUARE-LIST-R (EQUAL (CDR (CUTIL::SQUARE-LIST-R CUTIL::X)) (CUTIL::SQUARE-LIST-R (CDR CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-R-UNDER-IFF (IFF (CUTIL::SQUARE-LIST-R CUTIL::X) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-R-OF-LIST-FIX (EQUAL (CUTIL::SQUARE-LIST-R (LIST-FIX CUTIL::X)) (CUTIL::SQUARE-LIST-R CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-R-OF-APPEND (EQUAL (CUTIL::SQUARE-LIST-R (APPEND CUTIL::X CUTIL::Y)) (APPEND (CUTIL::SQUARE-LIST-R CUTIL::X) (CUTIL::SQUARE-LIST-R CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-R-OF-REV (EQUAL (CUTIL::SQUARE-LIST-R (REV CUTIL::X)) (REV (CUTIL::SQUARE-LIST-R CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R-OF-APPEND CUTIL::SQUARE-LIST-R-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-R-OF-REVAPPEND (EQUAL (CUTIL::SQUARE-LIST-R (REVAPPEND CUTIL::X CUTIL::Y)) (REVAPPEND (CUTIL::SQUARE-LIST-R CUTIL::X) (CUTIL::SQUARE-LIST-R CUTIL::Y))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R-OF-APPEND CUTIL::SQUARE-LIST-R-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::NTHCDR-OF-SQUARE-LIST-R (EQUAL (NTHCDR CUTIL::N (CUTIL::SQUARE-LIST-R CUTIL::X)) (CUTIL::SQUARE-LIST-R (NTHCDR CUTIL::N CUTIL::X))) :HINTS (("Goal" :INDUCT (NTHCDR CUTIL::N CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (NTHCDR CUTIL::SQUARE-LIST-R-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MEMBER-EQUAL-OF-SQUARE-IN-SQUARE-LIST-R-WHEN-MEMBER-EQUAL (IMPLIES (MEMBER-EQUAL CUTIL::A (DOUBLE-REWRITE CUTIL::X)) (MEMBER-EQUAL (CUTIL::SQUARE CUTIL::A) (CUTIL::SQUARE-LIST-R CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (MEMBER-EQUAL CUTIL::SQUARE-LIST-R-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SUBSETP-EQUAL-OF-SQUARE-LIST-RS-WHEN-SUBSETP-EQUAL (IMPLIES (SUBSETP-EQUAL (DOUBLE-REWRITE CUTIL::X) (DOUBLE-REWRITE CUTIL::Y)) (SUBSETP-EQUAL (CUTIL::SQUARE-LIST-R CUTIL::X) (CUTIL::SQUARE-LIST-R CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (SUBSETP-EQUAL CUTIL::MEMBER-EQUAL-OF-SQUARE-IN-SQUARE-LIST-R-WHEN-MEMBER-EQUAL CUTIL::SQUARE-LIST-R-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-R-EXEC-REMOVAL (EQUAL (CUTIL::SQUARE-LIST-R-EXEC CUTIL::X CUTIL::ACC) (REVAPPEND (CUTIL::SQUARE-LIST-R CUTIL::X) CUTIL::ACC)) :HINTS (("Goal" :INDUCT (CUTIL::SQUARE-LIST-R-EXEC CUTIL::X CUTIL::ACC) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R-EXEC CUTIL::SQUARE-LIST-R-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (VERIFY-GUARDS CUTIL::SQUARE-LIST-R-EXEC :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R-EXEC)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (VERIFY-GUARDS CUTIL::SQUARE-LIST-R :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R CUTIL::SQUARE-LIST-R-EXEC-REMOVAL CUTIL::TRUE-LISTP-OF-SQUARE-LIST-R REVERSE-REMOVAL REVAPPEND-REMOVAL REV-OF-APPEND REV-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (LOCAL (IN-THEORY (ENABLE CUTIL::SQUARE-LIST-R CUTIL::SQUARE-LIST-R-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R-OF-CONS))) (DEFTHM CUTIL::INTEGER-LISTP-OF-SQUARE-LIST-R (IMPLIES (FORCE (INTEGER-LISTP CUTIL::X)) (INTEGER-LISTP (CUTIL::SQUARE-LIST-R CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (ENABLE (:INDUCTION LEN))))))) (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (LOGIC) (DEFUND CUTIL::SQUARE-LIST-R-EXEC (CUTIL::X CUTIL::ACC) (DECLARE (XARGS :GUARD (INTEGER-LISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (IF (CONSP CUTIL::X) (CUTIL::SQUARE-LIST-R-EXEC (CDR CUTIL::X) (CONS (CUTIL::SQUARE (CAR CUTIL::X)) CUTIL::ACC)) CUTIL::ACC)) (DEFUND CUTIL::SQUARE-LIST-R (CUTIL::X) (DECLARE (XARGS :GUARD (INTEGER-LISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (MBE :LOGIC (IF (CONSP CUTIL::X) (CONS (CUTIL::SQUARE (CAR CUTIL::X)) (CUTIL::SQUARE-LIST-R (CDR CUTIL::X))) NIL) :EXEC (REVERSE (CUTIL::SQUARE-LIST-R-EXEC CUTIL::X NIL)))) (SET-INHIBIT-WARNINGS "disable") (RECORD-EXPANSION (LOCAL (MAKE-EVENT (IF (CUTIL::IS-THEOREM-P (QUOTE CUTIL::SQUARE-LIST-R-NIL-PRESERVINGP-LEMMA) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (DEFTHM CUTIL::SQUARE-LIST-R-NIL-PRESERVINGP-LEMMA (OR (EQUAL (ALISTP CUTIL::X) T) (EQUAL (ALISTP CUTIL::X) NIL)) :RULE-CLASSES :TYPE-PRESCRIPTION :HINTS (("Goal" :IN-THEORY (QUOTE ((:TYPE-PRESCRIPTION ALISTP))))))))))) (LOCAL (VALUE-TRIPLE :ELIDED))) (DEFTHM CUTIL::SQUARE-LIST-R-WHEN-NOT-CONSP (IMPLIES (NOT (CONSP CUTIL::X)) (EQUAL (CUTIL::SQUARE-LIST-R CUTIL::X) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-R-OF-CONS (EQUAL (CUTIL::SQUARE-LIST-R (CONS CUTIL::A CUTIL::X)) (CONS (CUTIL::SQUARE CUTIL::A) (CUTIL::SQUARE-LIST-R CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::TRUE-LISTP-OF-SQUARE-LIST-R (EQUAL (TRUE-LISTP (CUTIL::SQUARE-LIST-R CUTIL::X)) T) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::LEN-OF-SQUARE-LIST-R (EQUAL (LEN (CUTIL::SQUARE-LIST-R CUTIL::X)) (LEN CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CONSP-OF-SQUARE-LIST-R (EQUAL (CONSP (CUTIL::SQUARE-LIST-R CUTIL::X)) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CAR-OF-SQUARE-LIST-R (EQUAL (CAR (CUTIL::SQUARE-LIST-R CUTIL::X)) (IF (CONSP CUTIL::X) (CUTIL::SQUARE (CAR CUTIL::X)) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CDR-OF-SQUARE-LIST-R (EQUAL (CDR (CUTIL::SQUARE-LIST-R CUTIL::X)) (CUTIL::SQUARE-LIST-R (CDR CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-R-UNDER-IFF (IFF (CUTIL::SQUARE-LIST-R CUTIL::X) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-R-OF-LIST-FIX (EQUAL (CUTIL::SQUARE-LIST-R (LIST-FIX CUTIL::X)) (CUTIL::SQUARE-LIST-R CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-R-OF-APPEND (EQUAL (CUTIL::SQUARE-LIST-R (APPEND CUTIL::X CUTIL::Y)) (APPEND (CUTIL::SQUARE-LIST-R CUTIL::X) (CUTIL::SQUARE-LIST-R CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-R-OF-REV (EQUAL (CUTIL::SQUARE-LIST-R (REV CUTIL::X)) (REV (CUTIL::SQUARE-LIST-R CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R-OF-APPEND CUTIL::SQUARE-LIST-R-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-R-OF-REVAPPEND (EQUAL (CUTIL::SQUARE-LIST-R (REVAPPEND CUTIL::X CUTIL::Y)) (REVAPPEND (CUTIL::SQUARE-LIST-R CUTIL::X) (CUTIL::SQUARE-LIST-R CUTIL::Y))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R-OF-APPEND CUTIL::SQUARE-LIST-R-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::NTHCDR-OF-SQUARE-LIST-R (EQUAL (NTHCDR CUTIL::N (CUTIL::SQUARE-LIST-R CUTIL::X)) (CUTIL::SQUARE-LIST-R (NTHCDR CUTIL::N CUTIL::X))) :HINTS (("Goal" :INDUCT (NTHCDR CUTIL::N CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (NTHCDR CUTIL::SQUARE-LIST-R-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MEMBER-EQUAL-OF-SQUARE-IN-SQUARE-LIST-R-WHEN-MEMBER-EQUAL (IMPLIES (MEMBER-EQUAL CUTIL::A (DOUBLE-REWRITE CUTIL::X)) (MEMBER-EQUAL (CUTIL::SQUARE CUTIL::A) (CUTIL::SQUARE-LIST-R CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (MEMBER-EQUAL CUTIL::SQUARE-LIST-R-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SUBSETP-EQUAL-OF-SQUARE-LIST-RS-WHEN-SUBSETP-EQUAL (IMPLIES (SUBSETP-EQUAL (DOUBLE-REWRITE CUTIL::X) (DOUBLE-REWRITE CUTIL::Y)) (SUBSETP-EQUAL (CUTIL::SQUARE-LIST-R CUTIL::X) (CUTIL::SQUARE-LIST-R CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (SUBSETP-EQUAL CUTIL::MEMBER-EQUAL-OF-SQUARE-IN-SQUARE-LIST-R-WHEN-MEMBER-EQUAL CUTIL::SQUARE-LIST-R-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-R-EXEC-REMOVAL (EQUAL (CUTIL::SQUARE-LIST-R-EXEC CUTIL::X CUTIL::ACC) (REVAPPEND (CUTIL::SQUARE-LIST-R CUTIL::X) CUTIL::ACC)) :HINTS (("Goal" :INDUCT (CUTIL::SQUARE-LIST-R-EXEC CUTIL::X CUTIL::ACC) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R-EXEC CUTIL::SQUARE-LIST-R-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (VERIFY-GUARDS CUTIL::SQUARE-LIST-R-EXEC :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R-EXEC)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (VERIFY-GUARDS CUTIL::SQUARE-LIST-R :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R CUTIL::SQUARE-LIST-R-EXEC-REMOVAL CUTIL::TRUE-LISTP-OF-SQUARE-LIST-R REVERSE-REMOVAL REVAPPEND-REMOVAL REV-OF-APPEND REV-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (LOCAL (IN-THEORY (ENABLE CUTIL::SQUARE-LIST-R CUTIL::SQUARE-LIST-R-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R-OF-CONS))) (DEFTHM CUTIL::INTEGER-LISTP-OF-SQUARE-LIST-R (IMPLIES (FORCE (INTEGER-LISTP CUTIL::X)) (INTEGER-LISTP (CUTIL::SQUARE-LIST-R CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (ENABLE (:INDUCTION LEN)))))))) (RECORD-EXPANSION (MAKE-EVENT (LET* ((XDOC::NAME (QUOTE CUTIL::SQUARE-LIST-R)) (XDOC::PARENTS (QUOTE (UNDOCUMENTED))) (XDOC::SHORT (QUOTE "@(call SQUARE-LIST-R) maps @(see CUTIL::SQUARE) across a list.")) (XDOC::EXTENSION (QUOTE NIL)) (XDOC::WRLD (W STATE)) (XDOC::TRIPS (REVERSED-WORLD-SINCE-EVENT XDOC::WRLD (QUOTE (TABLE INTRO-TABLE :MARK (QUOTE CUTIL::SQUARE-LIST-R))) NIL)) (XDOC::INFO (REVERSE (NEW-FORMULA-INFO XDOC::TRIPS XDOC::WRLD NIL))) (XDOC::AUTODOC (XDOC::FORMULA-INFO-TO-DEFS (NOT XDOC::EXTENSION) XDOC::INFO)) (XDOC::LONG (CONCATENATE (QUOTE STRING) (QUOTE "<p>This is an ordinary @(see defprojection).</p>") (COERCE (LIST #\Newline #\Newline) (QUOTE STRING)) XDOC::AUTODOC))) (IF XDOC::EXTENSION (CONS (QUOTE XDOC-EXTEND) (CONS XDOC::EXTENSION (CONS XDOC::LONG (QUOTE NIL)))) (CONS (QUOTE DEFXDOC) (CONS XDOC::NAME (CONS (QUOTE :PARENTS) (CONS XDOC::PARENTS (CONS (QUOTE :SHORT) (CONS XDOC::SHORT (CONS (QUOTE :LONG) (CONS XDOC::LONG (QUOTE NIL)))))))))))) (WITH-OUTPUT :OFF (EVENT SUMMARY) (PROGN (TABLE XDOC (QUOTE DOC) (CONS (QUOTE ((:NAME . CUTIL::SQUARE-LIST-R) (:BASE-PKG . CUTIL::ACL2-PKG-WITNESS) (:PARENTS UNDOCUMENTED) (:SHORT . "@(call SQUARE-LIST-R) maps @(see CUTIL::SQUARE) across a list.") (:LONG . "<p>This is an ordinary @(see defprojection).</p>

<h3>Definitions and Theorems</h3>@(def |CUTIL|::|SQUARE-LIST-R-EXEC|)
@(def |CUTIL|::|SQUARE-LIST-R|)
@(def |CUTIL|::|SQUARE-LIST-R-WHEN-NOT-CONSP|)
@(def |CUTIL|::|SQUARE-LIST-R-OF-CONS|)
@(def |CUTIL|::|TRUE-LISTP-OF-SQUARE-LIST-R|)
@(def |CUTIL|::|LEN-OF-SQUARE-LIST-R|)
@(def |CUTIL|::|CONSP-OF-SQUARE-LIST-R|)
@(def |CUTIL|::|CAR-OF-SQUARE-LIST-R|)
@(def |CUTIL|::|CDR-OF-SQUARE-LIST-R|)
@(def |CUTIL|::|SQUARE-LIST-R-UNDER-IFF|)
@(def |CUTIL|::|SQUARE-LIST-R-OF-LIST-FIX|)
@(def |CUTIL|::|SQUARE-LIST-R-OF-APPEND|)
@(def |CUTIL|::|SQUARE-LIST-R-OF-REV|)
@(def |CUTIL|::|SQUARE-LIST-R-OF-REVAPPEND|)
@(def |CUTIL|::|NTHCDR-OF-SQUARE-LIST-R|)
@(def |CUTIL|::|MEMBER-EQUAL-OF-SQUARE-IN-SQUARE-LIST-R-WHEN-MEMBER-EQUAL|)
@(def |CUTIL|::|SUBSETP-EQUAL-OF-SQUARE-LIST-RS-WHEN-SUBSETP-EQUAL|)
@(def |CUTIL|::|SQUARE-LIST-R-EXEC-REMOVAL|)
@(def |CUTIL|::|INTEGER-LISTP-OF-SQUARE-LIST-R|)") (:FROM . "[books]/cutil/defprojection-tests.lisp"))) (XDOC::GET-XDOC-TABLE WORLD))) (VALUE-TRIPLE (QUOTE (DEFXDOC CUTIL::SQUARE-LIST-R)))))) (VALUE-TRIPLE (QUOTE CUTIL::SQUARE-LIST-R))))) (19 RECORD-EXPANSION (CUTIL::DEFPROJECTION CUTIL::SQUARE-LIST-R2 (CUTIL::X) (CUTIL::SQUARE CUTIL::X) :GUARD (INTEGER-LISTP CUTIL::X) :RESULT-TYPE INTEGER-LISTP :OPTIMIZE NIL :PARALLELIZE T) (WITH-OUTPUT :STACK :PUSH :OFF :ALL :ON ERROR (PROGN (TABLE INTRO-TABLE :MARK (QUOTE CUTIL::SQUARE-LIST-R2)) (RECORD-EXPANSION (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (LOGIC) (DEFUND CUTIL::SQUARE-LIST-R2-EXEC (CUTIL::X CUTIL::ACC) (DECLARE (XARGS :GUARD (INTEGER-LISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (IF (CONSP CUTIL::X) (CUTIL::SQUARE-LIST-R2-EXEC (CDR CUTIL::X) (CONS (CUTIL::SQUARE (CAR CUTIL::X)) CUTIL::ACC)) CUTIL::ACC)) (DEFUND CUTIL::SQUARE-LIST-R2 (CUTIL::X) (DECLARE (XARGS :GUARD (INTEGER-LISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (IF (CONSP CUTIL::X) (PARGS (CONS (CUTIL::SQUARE (CAR CUTIL::X)) (CUTIL::SQUARE-LIST-R2 (CDR CUTIL::X)))) NIL)) (SET-INHIBIT-WARNINGS "disable") (LOCAL (MAKE-EVENT (IF (CUTIL::IS-THEOREM-P (QUOTE CUTIL::SQUARE-LIST-R2-NIL-PRESERVINGP-LEMMA) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (DEFTHM CUTIL::SQUARE-LIST-R2-NIL-PRESERVINGP-LEMMA (OR (EQUAL (ALISTP CUTIL::X) T) (EQUAL (ALISTP CUTIL::X) NIL)) :RULE-CLASSES :TYPE-PRESCRIPTION :HINTS (("Goal" :IN-THEORY (QUOTE ((:TYPE-PRESCRIPTION ALISTP))))))))))) (DEFTHM CUTIL::SQUARE-LIST-R2-WHEN-NOT-CONSP (IMPLIES (NOT (CONSP CUTIL::X)) (EQUAL (CUTIL::SQUARE-LIST-R2 CUTIL::X) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R2)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-R2-OF-CONS (EQUAL (CUTIL::SQUARE-LIST-R2 (CONS CUTIL::A CUTIL::X)) (CONS (CUTIL::SQUARE CUTIL::A) (CUTIL::SQUARE-LIST-R2 CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R2)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::TRUE-LISTP-OF-SQUARE-LIST-R2 (EQUAL (TRUE-LISTP (CUTIL::SQUARE-LIST-R2 CUTIL::X)) T) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R2-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::LEN-OF-SQUARE-LIST-R2 (EQUAL (LEN (CUTIL::SQUARE-LIST-R2 CUTIL::X)) (LEN CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R2-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CONSP-OF-SQUARE-LIST-R2 (EQUAL (CONSP (CUTIL::SQUARE-LIST-R2 CUTIL::X)) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R2-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CAR-OF-SQUARE-LIST-R2 (EQUAL (CAR (CUTIL::SQUARE-LIST-R2 CUTIL::X)) (IF (CONSP CUTIL::X) (CUTIL::SQUARE (CAR CUTIL::X)) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R2-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CDR-OF-SQUARE-LIST-R2 (EQUAL (CDR (CUTIL::SQUARE-LIST-R2 CUTIL::X)) (CUTIL::SQUARE-LIST-R2 (CDR CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R2-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-R2-UNDER-IFF (IFF (CUTIL::SQUARE-LIST-R2 CUTIL::X) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R2-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-R2-OF-LIST-FIX (EQUAL (CUTIL::SQUARE-LIST-R2 (LIST-FIX CUTIL::X)) (CUTIL::SQUARE-LIST-R2 CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R2-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-R2-OF-APPEND (EQUAL (CUTIL::SQUARE-LIST-R2 (APPEND CUTIL::X CUTIL::Y)) (APPEND (CUTIL::SQUARE-LIST-R2 CUTIL::X) (CUTIL::SQUARE-LIST-R2 CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R2-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-R2-OF-REV (EQUAL (CUTIL::SQUARE-LIST-R2 (REV CUTIL::X)) (REV (CUTIL::SQUARE-LIST-R2 CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R2-OF-APPEND CUTIL::SQUARE-LIST-R2-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-R2-OF-REVAPPEND (EQUAL (CUTIL::SQUARE-LIST-R2 (REVAPPEND CUTIL::X CUTIL::Y)) (REVAPPEND (CUTIL::SQUARE-LIST-R2 CUTIL::X) (CUTIL::SQUARE-LIST-R2 CUTIL::Y))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R2-OF-APPEND CUTIL::SQUARE-LIST-R2-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::NTHCDR-OF-SQUARE-LIST-R2 (EQUAL (NTHCDR CUTIL::N (CUTIL::SQUARE-LIST-R2 CUTIL::X)) (CUTIL::SQUARE-LIST-R2 (NTHCDR CUTIL::N CUTIL::X))) :HINTS (("Goal" :INDUCT (NTHCDR CUTIL::N CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (NTHCDR CUTIL::SQUARE-LIST-R2-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MEMBER-EQUAL-OF-SQUARE-IN-SQUARE-LIST-R2-WHEN-MEMBER-EQUAL (IMPLIES (MEMBER-EQUAL CUTIL::A (DOUBLE-REWRITE CUTIL::X)) (MEMBER-EQUAL (CUTIL::SQUARE CUTIL::A) (CUTIL::SQUARE-LIST-R2 CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (MEMBER-EQUAL CUTIL::SQUARE-LIST-R2-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SUBSETP-EQUAL-OF-SQUARE-LIST-R2S-WHEN-SUBSETP-EQUAL (IMPLIES (SUBSETP-EQUAL (DOUBLE-REWRITE CUTIL::X) (DOUBLE-REWRITE CUTIL::Y)) (SUBSETP-EQUAL (CUTIL::SQUARE-LIST-R2 CUTIL::X) (CUTIL::SQUARE-LIST-R2 CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (SUBSETP-EQUAL CUTIL::MEMBER-EQUAL-OF-SQUARE-IN-SQUARE-LIST-R2-WHEN-MEMBER-EQUAL CUTIL::SQUARE-LIST-R2-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-R2-EXEC-REMOVAL (EQUAL (CUTIL::SQUARE-LIST-R2-EXEC CUTIL::X CUTIL::ACC) (REVAPPEND (CUTIL::SQUARE-LIST-R2 CUTIL::X) CUTIL::ACC)) :HINTS (("Goal" :INDUCT (CUTIL::SQUARE-LIST-R2-EXEC CUTIL::X CUTIL::ACC) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R2-EXEC CUTIL::SQUARE-LIST-R2-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (VERIFY-GUARDS CUTIL::SQUARE-LIST-R2-EXEC :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R2-EXEC)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (VERIFY-GUARDS CUTIL::SQUARE-LIST-R2 :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R2 CUTIL::SQUARE-LIST-R2-EXEC-REMOVAL CUTIL::TRUE-LISTP-OF-SQUARE-LIST-R2 REVERSE-REMOVAL REVAPPEND-REMOVAL REV-OF-APPEND REV-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (LOCAL (IN-THEORY (ENABLE CUTIL::SQUARE-LIST-R2 CUTIL::SQUARE-LIST-R2-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R2-OF-CONS))) (DEFTHM CUTIL::INTEGER-LISTP-OF-SQUARE-LIST-R2 (IMPLIES (FORCE (INTEGER-LISTP CUTIL::X)) (INTEGER-LISTP (CUTIL::SQUARE-LIST-R2 CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (ENABLE (:INDUCTION LEN))))))) (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (LOGIC) (DEFUND CUTIL::SQUARE-LIST-R2-EXEC (CUTIL::X CUTIL::ACC) (DECLARE (XARGS :GUARD (INTEGER-LISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (IF (CONSP CUTIL::X) (CUTIL::SQUARE-LIST-R2-EXEC (CDR CUTIL::X) (CONS (CUTIL::SQUARE (CAR CUTIL::X)) CUTIL::ACC)) CUTIL::ACC)) (DEFUND CUTIL::SQUARE-LIST-R2 (CUTIL::X) (DECLARE (XARGS :GUARD (INTEGER-LISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (IF (CONSP CUTIL::X) (PARGS (CONS (CUTIL::SQUARE (CAR CUTIL::X)) (CUTIL::SQUARE-LIST-R2 (CDR CUTIL::X)))) NIL)) (SET-INHIBIT-WARNINGS "disable") (RECORD-EXPANSION (LOCAL (MAKE-EVENT (IF (CUTIL::IS-THEOREM-P (QUOTE CUTIL::SQUARE-LIST-R2-NIL-PRESERVINGP-LEMMA) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (DEFTHM CUTIL::SQUARE-LIST-R2-NIL-PRESERVINGP-LEMMA (OR (EQUAL (ALISTP CUTIL::X) T) (EQUAL (ALISTP CUTIL::X) NIL)) :RULE-CLASSES :TYPE-PRESCRIPTION :HINTS (("Goal" :IN-THEORY (QUOTE ((:TYPE-PRESCRIPTION ALISTP))))))))))) (LOCAL (VALUE-TRIPLE :ELIDED))) (DEFTHM CUTIL::SQUARE-LIST-R2-WHEN-NOT-CONSP (IMPLIES (NOT (CONSP CUTIL::X)) (EQUAL (CUTIL::SQUARE-LIST-R2 CUTIL::X) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R2)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-R2-OF-CONS (EQUAL (CUTIL::SQUARE-LIST-R2 (CONS CUTIL::A CUTIL::X)) (CONS (CUTIL::SQUARE CUTIL::A) (CUTIL::SQUARE-LIST-R2 CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R2)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::TRUE-LISTP-OF-SQUARE-LIST-R2 (EQUAL (TRUE-LISTP (CUTIL::SQUARE-LIST-R2 CUTIL::X)) T) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R2-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::LEN-OF-SQUARE-LIST-R2 (EQUAL (LEN (CUTIL::SQUARE-LIST-R2 CUTIL::X)) (LEN CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R2-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CONSP-OF-SQUARE-LIST-R2 (EQUAL (CONSP (CUTIL::SQUARE-LIST-R2 CUTIL::X)) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R2-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CAR-OF-SQUARE-LIST-R2 (EQUAL (CAR (CUTIL::SQUARE-LIST-R2 CUTIL::X)) (IF (CONSP CUTIL::X) (CUTIL::SQUARE (CAR CUTIL::X)) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R2-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CDR-OF-SQUARE-LIST-R2 (EQUAL (CDR (CUTIL::SQUARE-LIST-R2 CUTIL::X)) (CUTIL::SQUARE-LIST-R2 (CDR CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R2-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-R2-UNDER-IFF (IFF (CUTIL::SQUARE-LIST-R2 CUTIL::X) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R2-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-R2-OF-LIST-FIX (EQUAL (CUTIL::SQUARE-LIST-R2 (LIST-FIX CUTIL::X)) (CUTIL::SQUARE-LIST-R2 CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R2-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-R2-OF-APPEND (EQUAL (CUTIL::SQUARE-LIST-R2 (APPEND CUTIL::X CUTIL::Y)) (APPEND (CUTIL::SQUARE-LIST-R2 CUTIL::X) (CUTIL::SQUARE-LIST-R2 CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R2-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-R2-OF-REV (EQUAL (CUTIL::SQUARE-LIST-R2 (REV CUTIL::X)) (REV (CUTIL::SQUARE-LIST-R2 CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R2-OF-APPEND CUTIL::SQUARE-LIST-R2-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-R2-OF-REVAPPEND (EQUAL (CUTIL::SQUARE-LIST-R2 (REVAPPEND CUTIL::X CUTIL::Y)) (REVAPPEND (CUTIL::SQUARE-LIST-R2 CUTIL::X) (CUTIL::SQUARE-LIST-R2 CUTIL::Y))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R2-OF-APPEND CUTIL::SQUARE-LIST-R2-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::NTHCDR-OF-SQUARE-LIST-R2 (EQUAL (NTHCDR CUTIL::N (CUTIL::SQUARE-LIST-R2 CUTIL::X)) (CUTIL::SQUARE-LIST-R2 (NTHCDR CUTIL::N CUTIL::X))) :HINTS (("Goal" :INDUCT (NTHCDR CUTIL::N CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (NTHCDR CUTIL::SQUARE-LIST-R2-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MEMBER-EQUAL-OF-SQUARE-IN-SQUARE-LIST-R2-WHEN-MEMBER-EQUAL (IMPLIES (MEMBER-EQUAL CUTIL::A (DOUBLE-REWRITE CUTIL::X)) (MEMBER-EQUAL (CUTIL::SQUARE CUTIL::A) (CUTIL::SQUARE-LIST-R2 CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (MEMBER-EQUAL CUTIL::SQUARE-LIST-R2-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SUBSETP-EQUAL-OF-SQUARE-LIST-R2S-WHEN-SUBSETP-EQUAL (IMPLIES (SUBSETP-EQUAL (DOUBLE-REWRITE CUTIL::X) (DOUBLE-REWRITE CUTIL::Y)) (SUBSETP-EQUAL (CUTIL::SQUARE-LIST-R2 CUTIL::X) (CUTIL::SQUARE-LIST-R2 CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (SUBSETP-EQUAL CUTIL::MEMBER-EQUAL-OF-SQUARE-IN-SQUARE-LIST-R2-WHEN-MEMBER-EQUAL CUTIL::SQUARE-LIST-R2-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SQUARE-LIST-R2-EXEC-REMOVAL (EQUAL (CUTIL::SQUARE-LIST-R2-EXEC CUTIL::X CUTIL::ACC) (REVAPPEND (CUTIL::SQUARE-LIST-R2 CUTIL::X) CUTIL::ACC)) :HINTS (("Goal" :INDUCT (CUTIL::SQUARE-LIST-R2-EXEC CUTIL::X CUTIL::ACC) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R2-EXEC CUTIL::SQUARE-LIST-R2-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (VERIFY-GUARDS CUTIL::SQUARE-LIST-R2-EXEC :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R2-EXEC)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (VERIFY-GUARDS CUTIL::SQUARE-LIST-R2 :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SQUARE-LIST-R2 CUTIL::SQUARE-LIST-R2-EXEC-REMOVAL CUTIL::TRUE-LISTP-OF-SQUARE-LIST-R2 REVERSE-REMOVAL REVAPPEND-REMOVAL REV-OF-APPEND REV-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (LOCAL (IN-THEORY (ENABLE CUTIL::SQUARE-LIST-R2 CUTIL::SQUARE-LIST-R2-WHEN-NOT-CONSP CUTIL::SQUARE-LIST-R2-OF-CONS))) (DEFTHM CUTIL::INTEGER-LISTP-OF-SQUARE-LIST-R2 (IMPLIES (FORCE (INTEGER-LISTP CUTIL::X)) (INTEGER-LISTP (CUTIL::SQUARE-LIST-R2 CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (ENABLE (:INDUCTION LEN)))))))) (RECORD-EXPANSION (MAKE-EVENT (LET* ((XDOC::NAME (QUOTE CUTIL::SQUARE-LIST-R2)) (XDOC::PARENTS (QUOTE (UNDOCUMENTED))) (XDOC::SHORT (QUOTE "@(call SQUARE-LIST-R2) maps @(see CUTIL::SQUARE) across a list.")) (XDOC::EXTENSION (QUOTE NIL)) (XDOC::WRLD (W STATE)) (XDOC::TRIPS (REVERSED-WORLD-SINCE-EVENT XDOC::WRLD (QUOTE (TABLE INTRO-TABLE :MARK (QUOTE CUTIL::SQUARE-LIST-R2))) NIL)) (XDOC::INFO (REVERSE (NEW-FORMULA-INFO XDOC::TRIPS XDOC::WRLD NIL))) (XDOC::AUTODOC (XDOC::FORMULA-INFO-TO-DEFS (NOT XDOC::EXTENSION) XDOC::INFO)) (XDOC::LONG (CONCATENATE (QUOTE STRING) (QUOTE "<p>This is an ordinary @(see defprojection).</p>") (COERCE (LIST #\Newline #\Newline) (QUOTE STRING)) XDOC::AUTODOC))) (IF XDOC::EXTENSION (CONS (QUOTE XDOC-EXTEND) (CONS XDOC::EXTENSION (CONS XDOC::LONG (QUOTE NIL)))) (CONS (QUOTE DEFXDOC) (CONS XDOC::NAME (CONS (QUOTE :PARENTS) (CONS XDOC::PARENTS (CONS (QUOTE :SHORT) (CONS XDOC::SHORT (CONS (QUOTE :LONG) (CONS XDOC::LONG (QUOTE NIL)))))))))))) (WITH-OUTPUT :OFF (EVENT SUMMARY) (PROGN (TABLE XDOC (QUOTE DOC) (CONS (QUOTE ((:NAME . CUTIL::SQUARE-LIST-R2) (:BASE-PKG . CUTIL::ACL2-PKG-WITNESS) (:PARENTS UNDOCUMENTED) (:SHORT . "@(call SQUARE-LIST-R2) maps @(see CUTIL::SQUARE) across a list.") (:LONG . "<p>This is an ordinary @(see defprojection).</p>

<h3>Definitions and Theorems</h3>@(def |CUTIL|::|SQUARE-LIST-R2-EXEC|)
@(def |CUTIL|::|SQUARE-LIST-R2|)
@(def |CUTIL|::|SQUARE-LIST-R2-WHEN-NOT-CONSP|)
@(def |CUTIL|::|SQUARE-LIST-R2-OF-CONS|)
@(def |CUTIL|::|TRUE-LISTP-OF-SQUARE-LIST-R2|)
@(def |CUTIL|::|LEN-OF-SQUARE-LIST-R2|)
@(def |CUTIL|::|CONSP-OF-SQUARE-LIST-R2|)
@(def |CUTIL|::|CAR-OF-SQUARE-LIST-R2|)
@(def |CUTIL|::|CDR-OF-SQUARE-LIST-R2|)
@(def |CUTIL|::|SQUARE-LIST-R2-UNDER-IFF|)
@(def |CUTIL|::|SQUARE-LIST-R2-OF-LIST-FIX|)
@(def |CUTIL|::|SQUARE-LIST-R2-OF-APPEND|)
@(def |CUTIL|::|SQUARE-LIST-R2-OF-REV|)
@(def |CUTIL|::|SQUARE-LIST-R2-OF-REVAPPEND|)
@(def |CUTIL|::|NTHCDR-OF-SQUARE-LIST-R2|)
@(def |CUTIL|::|MEMBER-EQUAL-OF-SQUARE-IN-SQUARE-LIST-R2-WHEN-MEMBER-EQUAL|)
@(def |CUTIL|::|SUBSETP-EQUAL-OF-SQUARE-LIST-R2S-WHEN-SUBSETP-EQUAL|)
@(def |CUTIL|::|SQUARE-LIST-R2-EXEC-REMOVAL|)
@(def |CUTIL|::|INTEGER-LISTP-OF-SQUARE-LIST-R2|)") (:FROM . "[books]/cutil/defprojection-tests.lisp"))) (XDOC::GET-XDOC-TABLE WORLD))) (VALUE-TRIPLE (QUOTE (DEFXDOC CUTIL::SQUARE-LIST-R2)))))) (VALUE-TRIPLE (QUOTE CUTIL::SQUARE-LIST-R2))))) (20 RECORD-EXPANSION (CUTIL::DEFPROJECTION CUTIL::ADD1-LIST (CUTIL::X) (+ 1 CUTIL::X) :GUARD (INTEGER-LISTP CUTIL::X) :PARENTS (CUTIL::FOO) :REST ((DEFTHM CUTIL::ADD1-LIST-INTEGER-LIST (IMPLIES (INTEGER-LISTP CUTIL::X) (INTEGER-LISTP (CUTIL::ADD1-LIST CUTIL::X)))))) (WITH-OUTPUT :STACK :PUSH :OFF :ALL :ON ERROR (PROGN (TABLE INTRO-TABLE :MARK (QUOTE CUTIL::ADD1-LIST)) (RECORD-EXPANSION (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (LOGIC) (DEFUND CUTIL::ADD1-LIST-EXEC (CUTIL::X CUTIL::ACC) (DECLARE (XARGS :GUARD (INTEGER-LISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (IF (CONSP CUTIL::X) (CUTIL::ADD1-LIST-EXEC (CDR CUTIL::X) (CONS (+ 1 (CAR CUTIL::X)) CUTIL::ACC)) CUTIL::ACC)) (DEFUND CUTIL::ADD1-LIST (CUTIL::X) (DECLARE (XARGS :GUARD (INTEGER-LISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (MBE :LOGIC (IF (CONSP CUTIL::X) (CONS (+ 1 (CAR CUTIL::X)) (CUTIL::ADD1-LIST (CDR CUTIL::X))) NIL) :EXEC (REVERSE (CUTIL::ADD1-LIST-EXEC CUTIL::X NIL)))) (SET-INHIBIT-WARNINGS "disable") (LOCAL (MAKE-EVENT (IF (CUTIL::IS-THEOREM-P (QUOTE CUTIL::ADD1-LIST-NIL-PRESERVINGP-LEMMA) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (DEFTHM CUTIL::ADD1-LIST-NIL-PRESERVINGP-LEMMA (OR (EQUAL (ALISTP CUTIL::X) T) (EQUAL (ALISTP CUTIL::X) NIL)) :RULE-CLASSES :TYPE-PRESCRIPTION :HINTS (("Goal" :IN-THEORY (QUOTE ((:TYPE-PRESCRIPTION ALISTP))))))))))) (DEFTHM CUTIL::ADD1-LIST-WHEN-NOT-CONSP (IMPLIES (NOT (CONSP CUTIL::X)) (EQUAL (CUTIL::ADD1-LIST CUTIL::X) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::ADD1-LIST)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::ADD1-LIST-OF-CONS (EQUAL (CUTIL::ADD1-LIST (CONS CUTIL::A CUTIL::X)) (CONS (+ 1 CUTIL::A) (CUTIL::ADD1-LIST CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::ADD1-LIST)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::TRUE-LISTP-OF-ADD1-LIST (EQUAL (TRUE-LISTP (CUTIL::ADD1-LIST CUTIL::X)) T) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::ADD1-LIST-WHEN-NOT-CONSP CUTIL::ADD1-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::LEN-OF-ADD1-LIST (EQUAL (LEN (CUTIL::ADD1-LIST CUTIL::X)) (LEN CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::ADD1-LIST-WHEN-NOT-CONSP CUTIL::ADD1-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CONSP-OF-ADD1-LIST (EQUAL (CONSP (CUTIL::ADD1-LIST CUTIL::X)) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::ADD1-LIST-WHEN-NOT-CONSP CUTIL::ADD1-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CAR-OF-ADD1-LIST (EQUAL (CAR (CUTIL::ADD1-LIST CUTIL::X)) (IF (CONSP CUTIL::X) (+ 1 (CAR CUTIL::X)) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::ADD1-LIST-WHEN-NOT-CONSP CUTIL::ADD1-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CDR-OF-ADD1-LIST (EQUAL (CDR (CUTIL::ADD1-LIST CUTIL::X)) (CUTIL::ADD1-LIST (CDR CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::ADD1-LIST-WHEN-NOT-CONSP CUTIL::ADD1-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::ADD1-LIST-UNDER-IFF (IFF (CUTIL::ADD1-LIST CUTIL::X) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::ADD1-LIST-WHEN-NOT-CONSP CUTIL::ADD1-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::ADD1-LIST-OF-LIST-FIX (EQUAL (CUTIL::ADD1-LIST (LIST-FIX CUTIL::X)) (CUTIL::ADD1-LIST CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::ADD1-LIST-WHEN-NOT-CONSP CUTIL::ADD1-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::ADD1-LIST-OF-APPEND (EQUAL (CUTIL::ADD1-LIST (APPEND CUTIL::X CUTIL::Y)) (APPEND (CUTIL::ADD1-LIST CUTIL::X) (CUTIL::ADD1-LIST CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::ADD1-LIST-WHEN-NOT-CONSP CUTIL::ADD1-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::ADD1-LIST-OF-REV (EQUAL (CUTIL::ADD1-LIST (REV CUTIL::X)) (REV (CUTIL::ADD1-LIST CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::ADD1-LIST-OF-APPEND CUTIL::ADD1-LIST-WHEN-NOT-CONSP CUTIL::ADD1-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::ADD1-LIST-OF-REVAPPEND (EQUAL (CUTIL::ADD1-LIST (REVAPPEND CUTIL::X CUTIL::Y)) (REVAPPEND (CUTIL::ADD1-LIST CUTIL::X) (CUTIL::ADD1-LIST CUTIL::Y))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::ADD1-LIST-OF-APPEND CUTIL::ADD1-LIST-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::NTHCDR-OF-ADD1-LIST (EQUAL (NTHCDR CUTIL::N (CUTIL::ADD1-LIST CUTIL::X)) (CUTIL::ADD1-LIST (NTHCDR CUTIL::N CUTIL::X))) :HINTS (("Goal" :INDUCT (NTHCDR CUTIL::N CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (NTHCDR CUTIL::ADD1-LIST-WHEN-NOT-CONSP CUTIL::ADD1-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MEMBER-EQUAL-OF-+-IN-ADD1-LIST-WHEN-MEMBER-EQUAL (IMPLIES (MEMBER-EQUAL CUTIL::A (DOUBLE-REWRITE CUTIL::X)) (MEMBER-EQUAL (+ 1 CUTIL::A) (CUTIL::ADD1-LIST CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (MEMBER-EQUAL CUTIL::ADD1-LIST-WHEN-NOT-CONSP CUTIL::ADD1-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SUBSETP-EQUAL-OF-ADD1-LISTS-WHEN-SUBSETP-EQUAL (IMPLIES (SUBSETP-EQUAL (DOUBLE-REWRITE CUTIL::X) (DOUBLE-REWRITE CUTIL::Y)) (SUBSETP-EQUAL (CUTIL::ADD1-LIST CUTIL::X) (CUTIL::ADD1-LIST CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (SUBSETP-EQUAL CUTIL::MEMBER-EQUAL-OF-+-IN-ADD1-LIST-WHEN-MEMBER-EQUAL CUTIL::ADD1-LIST-WHEN-NOT-CONSP CUTIL::ADD1-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::ADD1-LIST-EXEC-REMOVAL (EQUAL (CUTIL::ADD1-LIST-EXEC CUTIL::X CUTIL::ACC) (REVAPPEND (CUTIL::ADD1-LIST CUTIL::X) CUTIL::ACC)) :HINTS (("Goal" :INDUCT (CUTIL::ADD1-LIST-EXEC CUTIL::X CUTIL::ACC) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::ADD1-LIST-EXEC CUTIL::ADD1-LIST-WHEN-NOT-CONSP CUTIL::ADD1-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (VERIFY-GUARDS CUTIL::ADD1-LIST-EXEC :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::ADD1-LIST-EXEC)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (VERIFY-GUARDS CUTIL::ADD1-LIST :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::ADD1-LIST CUTIL::ADD1-LIST-EXEC-REMOVAL CUTIL::TRUE-LISTP-OF-ADD1-LIST REVERSE-REMOVAL REVAPPEND-REMOVAL REV-OF-APPEND REV-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (PROGN (MAKE-EVENT (IF (GLOBAL-VAL (QUOTE INCLUDE-BOOK-PATH) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::ADD1-LIST) (QUOTE (DEFUN CUTIL::ADD1-LIST (CUTIL::X) (NREVERSE (CUTIL::ADD1-LIST-EXEC CUTIL::X NIL)))))))))) (DEFTTAG CUTIL::CUTIL-OPTIMIZE) (NEVER-MEMOIZE CUTIL::ADD1-LIST-EXEC) (PROGN! (SET-RAW-MODE T) (DEFUN CUTIL::ADD1-LIST (CUTIL::X) (NREVERSE (CUTIL::ADD1-LIST-EXEC CUTIL::X NIL)))) (DEFTTAG NIL)) (LOCAL (IN-THEORY (ENABLE CUTIL::ADD1-LIST CUTIL::ADD1-LIST-WHEN-NOT-CONSP CUTIL::ADD1-LIST-OF-CONS))) (DEFTHM CUTIL::ADD1-LIST-INTEGER-LIST (IMPLIES (INTEGER-LISTP CUTIL::X) (INTEGER-LISTP (CUTIL::ADD1-LIST CUTIL::X)))))) (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (LOGIC) (DEFUND CUTIL::ADD1-LIST-EXEC (CUTIL::X CUTIL::ACC) (DECLARE (XARGS :GUARD (INTEGER-LISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (IF (CONSP CUTIL::X) (CUTIL::ADD1-LIST-EXEC (CDR CUTIL::X) (CONS (+ 1 (CAR CUTIL::X)) CUTIL::ACC)) CUTIL::ACC)) (DEFUND CUTIL::ADD1-LIST (CUTIL::X) (DECLARE (XARGS :GUARD (INTEGER-LISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (MBE :LOGIC (IF (CONSP CUTIL::X) (CONS (+ 1 (CAR CUTIL::X)) (CUTIL::ADD1-LIST (CDR CUTIL::X))) NIL) :EXEC (REVERSE (CUTIL::ADD1-LIST-EXEC CUTIL::X NIL)))) (SET-INHIBIT-WARNINGS "disable") (RECORD-EXPANSION (LOCAL (MAKE-EVENT (IF (CUTIL::IS-THEOREM-P (QUOTE CUTIL::ADD1-LIST-NIL-PRESERVINGP-LEMMA) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (DEFTHM CUTIL::ADD1-LIST-NIL-PRESERVINGP-LEMMA (OR (EQUAL (ALISTP CUTIL::X) T) (EQUAL (ALISTP CUTIL::X) NIL)) :RULE-CLASSES :TYPE-PRESCRIPTION :HINTS (("Goal" :IN-THEORY (QUOTE ((:TYPE-PRESCRIPTION ALISTP))))))))))) (LOCAL (VALUE-TRIPLE :ELIDED))) (DEFTHM CUTIL::ADD1-LIST-WHEN-NOT-CONSP (IMPLIES (NOT (CONSP CUTIL::X)) (EQUAL (CUTIL::ADD1-LIST CUTIL::X) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::ADD1-LIST)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::ADD1-LIST-OF-CONS (EQUAL (CUTIL::ADD1-LIST (CONS CUTIL::A CUTIL::X)) (CONS (+ 1 CUTIL::A) (CUTIL::ADD1-LIST CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::ADD1-LIST)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::TRUE-LISTP-OF-ADD1-LIST (EQUAL (TRUE-LISTP (CUTIL::ADD1-LIST CUTIL::X)) T) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::ADD1-LIST-WHEN-NOT-CONSP CUTIL::ADD1-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::LEN-OF-ADD1-LIST (EQUAL (LEN (CUTIL::ADD1-LIST CUTIL::X)) (LEN CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::ADD1-LIST-WHEN-NOT-CONSP CUTIL::ADD1-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CONSP-OF-ADD1-LIST (EQUAL (CONSP (CUTIL::ADD1-LIST CUTIL::X)) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::ADD1-LIST-WHEN-NOT-CONSP CUTIL::ADD1-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CAR-OF-ADD1-LIST (EQUAL (CAR (CUTIL::ADD1-LIST CUTIL::X)) (IF (CONSP CUTIL::X) (+ 1 (CAR CUTIL::X)) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::ADD1-LIST-WHEN-NOT-CONSP CUTIL::ADD1-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CDR-OF-ADD1-LIST (EQUAL (CDR (CUTIL::ADD1-LIST CUTIL::X)) (CUTIL::ADD1-LIST (CDR CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::ADD1-LIST-WHEN-NOT-CONSP CUTIL::ADD1-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::ADD1-LIST-UNDER-IFF (IFF (CUTIL::ADD1-LIST CUTIL::X) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::ADD1-LIST-WHEN-NOT-CONSP CUTIL::ADD1-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::ADD1-LIST-OF-LIST-FIX (EQUAL (CUTIL::ADD1-LIST (LIST-FIX CUTIL::X)) (CUTIL::ADD1-LIST CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::ADD1-LIST-WHEN-NOT-CONSP CUTIL::ADD1-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::ADD1-LIST-OF-APPEND (EQUAL (CUTIL::ADD1-LIST (APPEND CUTIL::X CUTIL::Y)) (APPEND (CUTIL::ADD1-LIST CUTIL::X) (CUTIL::ADD1-LIST CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::ADD1-LIST-WHEN-NOT-CONSP CUTIL::ADD1-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::ADD1-LIST-OF-REV (EQUAL (CUTIL::ADD1-LIST (REV CUTIL::X)) (REV (CUTIL::ADD1-LIST CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::ADD1-LIST-OF-APPEND CUTIL::ADD1-LIST-WHEN-NOT-CONSP CUTIL::ADD1-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::ADD1-LIST-OF-REVAPPEND (EQUAL (CUTIL::ADD1-LIST (REVAPPEND CUTIL::X CUTIL::Y)) (REVAPPEND (CUTIL::ADD1-LIST CUTIL::X) (CUTIL::ADD1-LIST CUTIL::Y))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::ADD1-LIST-OF-APPEND CUTIL::ADD1-LIST-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::NTHCDR-OF-ADD1-LIST (EQUAL (NTHCDR CUTIL::N (CUTIL::ADD1-LIST CUTIL::X)) (CUTIL::ADD1-LIST (NTHCDR CUTIL::N CUTIL::X))) :HINTS (("Goal" :INDUCT (NTHCDR CUTIL::N CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (NTHCDR CUTIL::ADD1-LIST-WHEN-NOT-CONSP CUTIL::ADD1-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MEMBER-EQUAL-OF-+-IN-ADD1-LIST-WHEN-MEMBER-EQUAL (IMPLIES (MEMBER-EQUAL CUTIL::A (DOUBLE-REWRITE CUTIL::X)) (MEMBER-EQUAL (+ 1 CUTIL::A) (CUTIL::ADD1-LIST CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (MEMBER-EQUAL CUTIL::ADD1-LIST-WHEN-NOT-CONSP CUTIL::ADD1-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SUBSETP-EQUAL-OF-ADD1-LISTS-WHEN-SUBSETP-EQUAL (IMPLIES (SUBSETP-EQUAL (DOUBLE-REWRITE CUTIL::X) (DOUBLE-REWRITE CUTIL::Y)) (SUBSETP-EQUAL (CUTIL::ADD1-LIST CUTIL::X) (CUTIL::ADD1-LIST CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (SUBSETP-EQUAL CUTIL::MEMBER-EQUAL-OF-+-IN-ADD1-LIST-WHEN-MEMBER-EQUAL CUTIL::ADD1-LIST-WHEN-NOT-CONSP CUTIL::ADD1-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::ADD1-LIST-EXEC-REMOVAL (EQUAL (CUTIL::ADD1-LIST-EXEC CUTIL::X CUTIL::ACC) (REVAPPEND (CUTIL::ADD1-LIST CUTIL::X) CUTIL::ACC)) :HINTS (("Goal" :INDUCT (CUTIL::ADD1-LIST-EXEC CUTIL::X CUTIL::ACC) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::ADD1-LIST-EXEC CUTIL::ADD1-LIST-WHEN-NOT-CONSP CUTIL::ADD1-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (VERIFY-GUARDS CUTIL::ADD1-LIST-EXEC :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::ADD1-LIST-EXEC)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (VERIFY-GUARDS CUTIL::ADD1-LIST :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::ADD1-LIST CUTIL::ADD1-LIST-EXEC-REMOVAL CUTIL::TRUE-LISTP-OF-ADD1-LIST REVERSE-REMOVAL REVAPPEND-REMOVAL REV-OF-APPEND REV-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (RECORD-EXPANSION (PROGN (MAKE-EVENT (IF (GLOBAL-VAL (QUOTE INCLUDE-BOOK-PATH) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::ADD1-LIST) (QUOTE (DEFUN CUTIL::ADD1-LIST (CUTIL::X) (NREVERSE (CUTIL::ADD1-LIST-EXEC CUTIL::X NIL)))))))))) (DEFTTAG CUTIL::CUTIL-OPTIMIZE) (NEVER-MEMOIZE CUTIL::ADD1-LIST-EXEC) (PROGN! (SET-RAW-MODE T) (DEFUN CUTIL::ADD1-LIST (CUTIL::X) (NREVERSE (CUTIL::ADD1-LIST-EXEC CUTIL::X NIL)))) (DEFTTAG NIL)) (PROGN (RECORD-EXPANSION (MAKE-EVENT (IF (GLOBAL-VAL (QUOTE INCLUDE-BOOK-PATH) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::ADD1-LIST) (QUOTE (DEFUN CUTIL::ADD1-LIST (CUTIL::X) (NREVERSE (CUTIL::ADD1-LIST-EXEC CUTIL::X NIL)))))))))) (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::ADD1-LIST) (QUOTE (DEFUN CUTIL::ADD1-LIST (CUTIL::X) (NREVERSE (CUTIL::ADD1-LIST-EXEC CUTIL::X NIL))))))) (DEFTTAG CUTIL::CUTIL-OPTIMIZE) (RECORD-EXPANSION (NEVER-MEMOIZE CUTIL::ADD1-LIST-EXEC) (MAKE-EVENT (PROG2$ (NEVER-MEMOIZE-FN (QUOTE CUTIL::ADD1-LIST-EXEC)) (QUOTE (VALUE-TRIPLE :INVISIBLE))) :CHECK-EXPANSION (VALUE-TRIPLE :INVISIBLE))) (PROGN! (SET-RAW-MODE T) (DEFUN CUTIL::ADD1-LIST (CUTIL::X) (NREVERSE (CUTIL::ADD1-LIST-EXEC CUTIL::X NIL)))) (DEFTTAG NIL))) (LOCAL (IN-THEORY (ENABLE CUTIL::ADD1-LIST CUTIL::ADD1-LIST-WHEN-NOT-CONSP CUTIL::ADD1-LIST-OF-CONS))) (DEFTHM CUTIL::ADD1-LIST-INTEGER-LIST (IMPLIES (INTEGER-LISTP CUTIL::X) (INTEGER-LISTP (CUTIL::ADD1-LIST CUTIL::X))))))) (RECORD-EXPANSION (MAKE-EVENT (LET* ((XDOC::NAME (QUOTE CUTIL::ADD1-LIST)) (XDOC::PARENTS (QUOTE (CUTIL::FOO))) (XDOC::SHORT (QUOTE "@(call ADD1-LIST) maps @(see COMMON-LISP::+) across a list.")) (XDOC::EXTENSION (QUOTE NIL)) (XDOC::WRLD (W STATE)) (XDOC::TRIPS (REVERSED-WORLD-SINCE-EVENT XDOC::WRLD (QUOTE (TABLE INTRO-TABLE :MARK (QUOTE CUTIL::ADD1-LIST))) NIL)) (XDOC::INFO (REVERSE (NEW-FORMULA-INFO XDOC::TRIPS XDOC::WRLD NIL))) (XDOC::AUTODOC (XDOC::FORMULA-INFO-TO-DEFS (NOT XDOC::EXTENSION) XDOC::INFO)) (XDOC::LONG (CONCATENATE (QUOTE STRING) (QUOTE "<p>This is an ordinary @(see defprojection).</p>") (COERCE (LIST #\Newline #\Newline) (QUOTE STRING)) XDOC::AUTODOC))) (IF XDOC::EXTENSION (CONS (QUOTE XDOC-EXTEND) (CONS XDOC::EXTENSION (CONS XDOC::LONG (QUOTE NIL)))) (CONS (QUOTE DEFXDOC) (CONS XDOC::NAME (CONS (QUOTE :PARENTS) (CONS XDOC::PARENTS (CONS (QUOTE :SHORT) (CONS XDOC::SHORT (CONS (QUOTE :LONG) (CONS XDOC::LONG (QUOTE NIL)))))))))))) (WITH-OUTPUT :OFF (EVENT SUMMARY) (PROGN (TABLE XDOC (QUOTE DOC) (CONS (QUOTE ((:NAME . CUTIL::ADD1-LIST) (:BASE-PKG . CUTIL::ACL2-PKG-WITNESS) (:PARENTS CUTIL::FOO) (:SHORT . "@(call ADD1-LIST) maps @(see COMMON-LISP::+) across a list.") (:LONG . "<p>This is an ordinary @(see defprojection).</p>

<h3>Definitions and Theorems</h3>@(def |CUTIL|::|ADD1-LIST-EXEC|)
@(def |CUTIL|::|ADD1-LIST|)
@(def |CUTIL|::|ADD1-LIST-WHEN-NOT-CONSP|)
@(def |CUTIL|::|ADD1-LIST-OF-CONS|)
@(def |CUTIL|::|TRUE-LISTP-OF-ADD1-LIST|)
@(def |CUTIL|::|LEN-OF-ADD1-LIST|)
@(def |CUTIL|::|CONSP-OF-ADD1-LIST|)
@(def |CUTIL|::|CAR-OF-ADD1-LIST|)
@(def |CUTIL|::|CDR-OF-ADD1-LIST|)
@(def |CUTIL|::|ADD1-LIST-UNDER-IFF|)
@(def |CUTIL|::|ADD1-LIST-OF-LIST-FIX|)
@(def |CUTIL|::|ADD1-LIST-OF-APPEND|)
@(def |CUTIL|::|ADD1-LIST-OF-REV|)
@(def |CUTIL|::|ADD1-LIST-OF-REVAPPEND|)
@(def |CUTIL|::|NTHCDR-OF-ADD1-LIST|)
@(def |CUTIL|::|MEMBER-EQUAL-OF-+-IN-ADD1-LIST-WHEN-MEMBER-EQUAL|)
@(def |CUTIL|::|SUBSETP-EQUAL-OF-ADD1-LISTS-WHEN-SUBSETP-EQUAL|)
@(def |CUTIL|::|ADD1-LIST-EXEC-REMOVAL|)
@(def |CUTIL|::|ADD1-LIST-INTEGER-LIST|)") (:FROM . "[books]/cutil/defprojection-tests.lisp"))) (XDOC::GET-XDOC-TABLE WORLD))) (VALUE-TRIPLE (QUOTE (DEFXDOC CUTIL::ADD1-LIST)))))) (VALUE-TRIPLE (QUOTE CUTIL::ADD1-LIST))))) (22 RECORD-EXPANSION (CUTIL::DEFPROJECTION CUTIL::SYMBOL-<-FOO-LIST (CUTIL::X) (SYMBOL-< :FOO CUTIL::X) :GUARD (SYMBOL-LISTP CUTIL::X)) (WITH-OUTPUT :STACK :PUSH :OFF :ALL :ON ERROR (PROGN (TABLE INTRO-TABLE :MARK (QUOTE CUTIL::SYMBOL-<-FOO-LIST)) (RECORD-EXPANSION (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (LOGIC) (DEFUND CUTIL::SYMBOL-<-FOO-LIST-EXEC (CUTIL::X CUTIL::ACC) (DECLARE (XARGS :GUARD (SYMBOL-LISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (IF (CONSP CUTIL::X) (CUTIL::SYMBOL-<-FOO-LIST-EXEC (CDR CUTIL::X) (CONS (SYMBOL-< :FOO (CAR CUTIL::X)) CUTIL::ACC)) CUTIL::ACC)) (DEFUND CUTIL::SYMBOL-<-FOO-LIST (CUTIL::X) (DECLARE (XARGS :GUARD (SYMBOL-LISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (MBE :LOGIC (IF (CONSP CUTIL::X) (CONS (SYMBOL-< :FOO (CAR CUTIL::X)) (CUTIL::SYMBOL-<-FOO-LIST (CDR CUTIL::X))) NIL) :EXEC (REVERSE (CUTIL::SYMBOL-<-FOO-LIST-EXEC CUTIL::X NIL)))) (SET-INHIBIT-WARNINGS "disable") (LOCAL (MAKE-EVENT (IF (CUTIL::IS-THEOREM-P (QUOTE CUTIL::SYMBOL-<-FOO-LIST-NIL-PRESERVINGP-LEMMA) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (DEFTHM CUTIL::SYMBOL-<-FOO-LIST-NIL-PRESERVINGP-LEMMA (OR (EQUAL (ALISTP CUTIL::X) T) (EQUAL (ALISTP CUTIL::X) NIL)) :RULE-CLASSES :TYPE-PRESCRIPTION :HINTS (("Goal" :IN-THEORY (QUOTE ((:TYPE-PRESCRIPTION ALISTP))))))))))) (DEFTHM CUTIL::SYMBOL-<-FOO-LIST-WHEN-NOT-CONSP (IMPLIES (NOT (CONSP CUTIL::X)) (EQUAL (CUTIL::SYMBOL-<-FOO-LIST CUTIL::X) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-FOO-LIST)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SYMBOL-<-FOO-LIST-OF-CONS (EQUAL (CUTIL::SYMBOL-<-FOO-LIST (CONS CUTIL::A CUTIL::X)) (CONS (SYMBOL-< :FOO CUTIL::A) (CUTIL::SYMBOL-<-FOO-LIST CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-FOO-LIST)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::TRUE-LISTP-OF-SYMBOL-<-FOO-LIST (EQUAL (TRUE-LISTP (CUTIL::SYMBOL-<-FOO-LIST CUTIL::X)) T) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-FOO-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-FOO-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::LEN-OF-SYMBOL-<-FOO-LIST (EQUAL (LEN (CUTIL::SYMBOL-<-FOO-LIST CUTIL::X)) (LEN CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-FOO-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-FOO-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CONSP-OF-SYMBOL-<-FOO-LIST (EQUAL (CONSP (CUTIL::SYMBOL-<-FOO-LIST CUTIL::X)) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-FOO-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-FOO-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CAR-OF-SYMBOL-<-FOO-LIST (EQUAL (CAR (CUTIL::SYMBOL-<-FOO-LIST CUTIL::X)) (IF (CONSP CUTIL::X) (SYMBOL-< :FOO (CAR CUTIL::X)) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-FOO-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-FOO-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CDR-OF-SYMBOL-<-FOO-LIST (EQUAL (CDR (CUTIL::SYMBOL-<-FOO-LIST CUTIL::X)) (CUTIL::SYMBOL-<-FOO-LIST (CDR CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-FOO-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-FOO-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SYMBOL-<-FOO-LIST-UNDER-IFF (IFF (CUTIL::SYMBOL-<-FOO-LIST CUTIL::X) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-FOO-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-FOO-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SYMBOL-<-FOO-LIST-OF-LIST-FIX (EQUAL (CUTIL::SYMBOL-<-FOO-LIST (LIST-FIX CUTIL::X)) (CUTIL::SYMBOL-<-FOO-LIST CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-FOO-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-FOO-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SYMBOL-<-FOO-LIST-OF-APPEND (EQUAL (CUTIL::SYMBOL-<-FOO-LIST (APPEND CUTIL::X CUTIL::Y)) (APPEND (CUTIL::SYMBOL-<-FOO-LIST CUTIL::X) (CUTIL::SYMBOL-<-FOO-LIST CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-FOO-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-FOO-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SYMBOL-<-FOO-LIST-OF-REV (EQUAL (CUTIL::SYMBOL-<-FOO-LIST (REV CUTIL::X)) (REV (CUTIL::SYMBOL-<-FOO-LIST CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-FOO-LIST-OF-APPEND CUTIL::SYMBOL-<-FOO-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-FOO-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SYMBOL-<-FOO-LIST-OF-REVAPPEND (EQUAL (CUTIL::SYMBOL-<-FOO-LIST (REVAPPEND CUTIL::X CUTIL::Y)) (REVAPPEND (CUTIL::SYMBOL-<-FOO-LIST CUTIL::X) (CUTIL::SYMBOL-<-FOO-LIST CUTIL::Y))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-FOO-LIST-OF-APPEND CUTIL::SYMBOL-<-FOO-LIST-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::NTHCDR-OF-SYMBOL-<-FOO-LIST (EQUAL (NTHCDR CUTIL::N (CUTIL::SYMBOL-<-FOO-LIST CUTIL::X)) (CUTIL::SYMBOL-<-FOO-LIST (NTHCDR CUTIL::N CUTIL::X))) :HINTS (("Goal" :INDUCT (NTHCDR CUTIL::N CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (NTHCDR CUTIL::SYMBOL-<-FOO-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-FOO-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MEMBER-EQUAL-OF-SYMBOL-<-IN-SYMBOL-<-FOO-LIST-WHEN-MEMBER-EQUAL (IMPLIES (MEMBER-EQUAL CUTIL::A (DOUBLE-REWRITE CUTIL::X)) (MEMBER-EQUAL (SYMBOL-< :FOO CUTIL::A) (CUTIL::SYMBOL-<-FOO-LIST CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (MEMBER-EQUAL CUTIL::SYMBOL-<-FOO-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-FOO-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SUBSETP-EQUAL-OF-SYMBOL-<-FOO-LISTS-WHEN-SUBSETP-EQUAL (IMPLIES (SUBSETP-EQUAL (DOUBLE-REWRITE CUTIL::X) (DOUBLE-REWRITE CUTIL::Y)) (SUBSETP-EQUAL (CUTIL::SYMBOL-<-FOO-LIST CUTIL::X) (CUTIL::SYMBOL-<-FOO-LIST CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (SUBSETP-EQUAL CUTIL::MEMBER-EQUAL-OF-SYMBOL-<-IN-SYMBOL-<-FOO-LIST-WHEN-MEMBER-EQUAL CUTIL::SYMBOL-<-FOO-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-FOO-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SYMBOL-<-FOO-LIST-EXEC-REMOVAL (EQUAL (CUTIL::SYMBOL-<-FOO-LIST-EXEC CUTIL::X CUTIL::ACC) (REVAPPEND (CUTIL::SYMBOL-<-FOO-LIST CUTIL::X) CUTIL::ACC)) :HINTS (("Goal" :INDUCT (CUTIL::SYMBOL-<-FOO-LIST-EXEC CUTIL::X CUTIL::ACC) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-FOO-LIST-EXEC CUTIL::SYMBOL-<-FOO-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-FOO-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (VERIFY-GUARDS CUTIL::SYMBOL-<-FOO-LIST-EXEC :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-FOO-LIST-EXEC)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (VERIFY-GUARDS CUTIL::SYMBOL-<-FOO-LIST :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-FOO-LIST CUTIL::SYMBOL-<-FOO-LIST-EXEC-REMOVAL CUTIL::TRUE-LISTP-OF-SYMBOL-<-FOO-LIST REVERSE-REMOVAL REVAPPEND-REMOVAL REV-OF-APPEND REV-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (PROGN (MAKE-EVENT (IF (GLOBAL-VAL (QUOTE INCLUDE-BOOK-PATH) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::SYMBOL-<-FOO-LIST) (QUOTE (DEFUN CUTIL::SYMBOL-<-FOO-LIST (CUTIL::X) (NREVERSE (CUTIL::SYMBOL-<-FOO-LIST-EXEC CUTIL::X NIL)))))))))) (DEFTTAG CUTIL::CUTIL-OPTIMIZE) (NEVER-MEMOIZE CUTIL::SYMBOL-<-FOO-LIST-EXEC) (PROGN! (SET-RAW-MODE T) (DEFUN CUTIL::SYMBOL-<-FOO-LIST (CUTIL::X) (NREVERSE (CUTIL::SYMBOL-<-FOO-LIST-EXEC CUTIL::X NIL)))) (DEFTTAG NIL)) (LOCAL (IN-THEORY (ENABLE CUTIL::SYMBOL-<-FOO-LIST CUTIL::SYMBOL-<-FOO-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-FOO-LIST-OF-CONS))))) (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (LOGIC) (DEFUND CUTIL::SYMBOL-<-FOO-LIST-EXEC (CUTIL::X CUTIL::ACC) (DECLARE (XARGS :GUARD (SYMBOL-LISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (IF (CONSP CUTIL::X) (CUTIL::SYMBOL-<-FOO-LIST-EXEC (CDR CUTIL::X) (CONS (SYMBOL-< :FOO (CAR CUTIL::X)) CUTIL::ACC)) CUTIL::ACC)) (DEFUND CUTIL::SYMBOL-<-FOO-LIST (CUTIL::X) (DECLARE (XARGS :GUARD (SYMBOL-LISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (MBE :LOGIC (IF (CONSP CUTIL::X) (CONS (SYMBOL-< :FOO (CAR CUTIL::X)) (CUTIL::SYMBOL-<-FOO-LIST (CDR CUTIL::X))) NIL) :EXEC (REVERSE (CUTIL::SYMBOL-<-FOO-LIST-EXEC CUTIL::X NIL)))) (SET-INHIBIT-WARNINGS "disable") (RECORD-EXPANSION (LOCAL (MAKE-EVENT (IF (CUTIL::IS-THEOREM-P (QUOTE CUTIL::SYMBOL-<-FOO-LIST-NIL-PRESERVINGP-LEMMA) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (DEFTHM CUTIL::SYMBOL-<-FOO-LIST-NIL-PRESERVINGP-LEMMA (OR (EQUAL (ALISTP CUTIL::X) T) (EQUAL (ALISTP CUTIL::X) NIL)) :RULE-CLASSES :TYPE-PRESCRIPTION :HINTS (("Goal" :IN-THEORY (QUOTE ((:TYPE-PRESCRIPTION ALISTP))))))))))) (LOCAL (VALUE-TRIPLE :ELIDED))) (DEFTHM CUTIL::SYMBOL-<-FOO-LIST-WHEN-NOT-CONSP (IMPLIES (NOT (CONSP CUTIL::X)) (EQUAL (CUTIL::SYMBOL-<-FOO-LIST CUTIL::X) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-FOO-LIST)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SYMBOL-<-FOO-LIST-OF-CONS (EQUAL (CUTIL::SYMBOL-<-FOO-LIST (CONS CUTIL::A CUTIL::X)) (CONS (SYMBOL-< :FOO CUTIL::A) (CUTIL::SYMBOL-<-FOO-LIST CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-FOO-LIST)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::TRUE-LISTP-OF-SYMBOL-<-FOO-LIST (EQUAL (TRUE-LISTP (CUTIL::SYMBOL-<-FOO-LIST CUTIL::X)) T) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-FOO-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-FOO-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::LEN-OF-SYMBOL-<-FOO-LIST (EQUAL (LEN (CUTIL::SYMBOL-<-FOO-LIST CUTIL::X)) (LEN CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-FOO-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-FOO-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CONSP-OF-SYMBOL-<-FOO-LIST (EQUAL (CONSP (CUTIL::SYMBOL-<-FOO-LIST CUTIL::X)) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-FOO-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-FOO-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CAR-OF-SYMBOL-<-FOO-LIST (EQUAL (CAR (CUTIL::SYMBOL-<-FOO-LIST CUTIL::X)) (IF (CONSP CUTIL::X) (SYMBOL-< :FOO (CAR CUTIL::X)) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-FOO-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-FOO-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CDR-OF-SYMBOL-<-FOO-LIST (EQUAL (CDR (CUTIL::SYMBOL-<-FOO-LIST CUTIL::X)) (CUTIL::SYMBOL-<-FOO-LIST (CDR CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-FOO-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-FOO-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SYMBOL-<-FOO-LIST-UNDER-IFF (IFF (CUTIL::SYMBOL-<-FOO-LIST CUTIL::X) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-FOO-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-FOO-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SYMBOL-<-FOO-LIST-OF-LIST-FIX (EQUAL (CUTIL::SYMBOL-<-FOO-LIST (LIST-FIX CUTIL::X)) (CUTIL::SYMBOL-<-FOO-LIST CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-FOO-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-FOO-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SYMBOL-<-FOO-LIST-OF-APPEND (EQUAL (CUTIL::SYMBOL-<-FOO-LIST (APPEND CUTIL::X CUTIL::Y)) (APPEND (CUTIL::SYMBOL-<-FOO-LIST CUTIL::X) (CUTIL::SYMBOL-<-FOO-LIST CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-FOO-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-FOO-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SYMBOL-<-FOO-LIST-OF-REV (EQUAL (CUTIL::SYMBOL-<-FOO-LIST (REV CUTIL::X)) (REV (CUTIL::SYMBOL-<-FOO-LIST CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-FOO-LIST-OF-APPEND CUTIL::SYMBOL-<-FOO-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-FOO-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SYMBOL-<-FOO-LIST-OF-REVAPPEND (EQUAL (CUTIL::SYMBOL-<-FOO-LIST (REVAPPEND CUTIL::X CUTIL::Y)) (REVAPPEND (CUTIL::SYMBOL-<-FOO-LIST CUTIL::X) (CUTIL::SYMBOL-<-FOO-LIST CUTIL::Y))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-FOO-LIST-OF-APPEND CUTIL::SYMBOL-<-FOO-LIST-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::NTHCDR-OF-SYMBOL-<-FOO-LIST (EQUAL (NTHCDR CUTIL::N (CUTIL::SYMBOL-<-FOO-LIST CUTIL::X)) (CUTIL::SYMBOL-<-FOO-LIST (NTHCDR CUTIL::N CUTIL::X))) :HINTS (("Goal" :INDUCT (NTHCDR CUTIL::N CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (NTHCDR CUTIL::SYMBOL-<-FOO-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-FOO-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MEMBER-EQUAL-OF-SYMBOL-<-IN-SYMBOL-<-FOO-LIST-WHEN-MEMBER-EQUAL (IMPLIES (MEMBER-EQUAL CUTIL::A (DOUBLE-REWRITE CUTIL::X)) (MEMBER-EQUAL (SYMBOL-< :FOO CUTIL::A) (CUTIL::SYMBOL-<-FOO-LIST CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (MEMBER-EQUAL CUTIL::SYMBOL-<-FOO-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-FOO-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SUBSETP-EQUAL-OF-SYMBOL-<-FOO-LISTS-WHEN-SUBSETP-EQUAL (IMPLIES (SUBSETP-EQUAL (DOUBLE-REWRITE CUTIL::X) (DOUBLE-REWRITE CUTIL::Y)) (SUBSETP-EQUAL (CUTIL::SYMBOL-<-FOO-LIST CUTIL::X) (CUTIL::SYMBOL-<-FOO-LIST CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (SUBSETP-EQUAL CUTIL::MEMBER-EQUAL-OF-SYMBOL-<-IN-SYMBOL-<-FOO-LIST-WHEN-MEMBER-EQUAL CUTIL::SYMBOL-<-FOO-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-FOO-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SYMBOL-<-FOO-LIST-EXEC-REMOVAL (EQUAL (CUTIL::SYMBOL-<-FOO-LIST-EXEC CUTIL::X CUTIL::ACC) (REVAPPEND (CUTIL::SYMBOL-<-FOO-LIST CUTIL::X) CUTIL::ACC)) :HINTS (("Goal" :INDUCT (CUTIL::SYMBOL-<-FOO-LIST-EXEC CUTIL::X CUTIL::ACC) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-FOO-LIST-EXEC CUTIL::SYMBOL-<-FOO-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-FOO-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (VERIFY-GUARDS CUTIL::SYMBOL-<-FOO-LIST-EXEC :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-FOO-LIST-EXEC)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (VERIFY-GUARDS CUTIL::SYMBOL-<-FOO-LIST :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-FOO-LIST CUTIL::SYMBOL-<-FOO-LIST-EXEC-REMOVAL CUTIL::TRUE-LISTP-OF-SYMBOL-<-FOO-LIST REVERSE-REMOVAL REVAPPEND-REMOVAL REV-OF-APPEND REV-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (RECORD-EXPANSION (PROGN (MAKE-EVENT (IF (GLOBAL-VAL (QUOTE INCLUDE-BOOK-PATH) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::SYMBOL-<-FOO-LIST) (QUOTE (DEFUN CUTIL::SYMBOL-<-FOO-LIST (CUTIL::X) (NREVERSE (CUTIL::SYMBOL-<-FOO-LIST-EXEC CUTIL::X NIL)))))))))) (DEFTTAG CUTIL::CUTIL-OPTIMIZE) (NEVER-MEMOIZE CUTIL::SYMBOL-<-FOO-LIST-EXEC) (PROGN! (SET-RAW-MODE T) (DEFUN CUTIL::SYMBOL-<-FOO-LIST (CUTIL::X) (NREVERSE (CUTIL::SYMBOL-<-FOO-LIST-EXEC CUTIL::X NIL)))) (DEFTTAG NIL)) (PROGN (RECORD-EXPANSION (MAKE-EVENT (IF (GLOBAL-VAL (QUOTE INCLUDE-BOOK-PATH) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::SYMBOL-<-FOO-LIST) (QUOTE (DEFUN CUTIL::SYMBOL-<-FOO-LIST (CUTIL::X) (NREVERSE (CUTIL::SYMBOL-<-FOO-LIST-EXEC CUTIL::X NIL)))))))))) (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::SYMBOL-<-FOO-LIST) (QUOTE (DEFUN CUTIL::SYMBOL-<-FOO-LIST (CUTIL::X) (NREVERSE (CUTIL::SYMBOL-<-FOO-LIST-EXEC CUTIL::X NIL))))))) (DEFTTAG CUTIL::CUTIL-OPTIMIZE) (RECORD-EXPANSION (NEVER-MEMOIZE CUTIL::SYMBOL-<-FOO-LIST-EXEC) (MAKE-EVENT (PROG2$ (NEVER-MEMOIZE-FN (QUOTE CUTIL::SYMBOL-<-FOO-LIST-EXEC)) (QUOTE (VALUE-TRIPLE :INVISIBLE))) :CHECK-EXPANSION (VALUE-TRIPLE :INVISIBLE))) (PROGN! (SET-RAW-MODE T) (DEFUN CUTIL::SYMBOL-<-FOO-LIST (CUTIL::X) (NREVERSE (CUTIL::SYMBOL-<-FOO-LIST-EXEC CUTIL::X NIL)))) (DEFTTAG NIL))) (LOCAL (IN-THEORY (ENABLE CUTIL::SYMBOL-<-FOO-LIST CUTIL::SYMBOL-<-FOO-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-FOO-LIST-OF-CONS)))))) (RECORD-EXPANSION (MAKE-EVENT (LET* ((XDOC::NAME (QUOTE CUTIL::SYMBOL-<-FOO-LIST)) (XDOC::PARENTS (QUOTE (UNDOCUMENTED))) (XDOC::SHORT (QUOTE "@(call SYMBOL-<-FOO-LIST) maps @(see ACL2::SYMBOL-<) across a list.")) (XDOC::EXTENSION (QUOTE NIL)) (XDOC::WRLD (W STATE)) (XDOC::TRIPS (REVERSED-WORLD-SINCE-EVENT XDOC::WRLD (QUOTE (TABLE INTRO-TABLE :MARK (QUOTE CUTIL::SYMBOL-<-FOO-LIST))) NIL)) (XDOC::INFO (REVERSE (NEW-FORMULA-INFO XDOC::TRIPS XDOC::WRLD NIL))) (XDOC::AUTODOC (XDOC::FORMULA-INFO-TO-DEFS (NOT XDOC::EXTENSION) XDOC::INFO)) (XDOC::LONG (CONCATENATE (QUOTE STRING) (QUOTE "<p>This is an ordinary @(see defprojection).</p>") (COERCE (LIST #\Newline #\Newline) (QUOTE STRING)) XDOC::AUTODOC))) (IF XDOC::EXTENSION (CONS (QUOTE XDOC-EXTEND) (CONS XDOC::EXTENSION (CONS XDOC::LONG (QUOTE NIL)))) (CONS (QUOTE DEFXDOC) (CONS XDOC::NAME (CONS (QUOTE :PARENTS) (CONS XDOC::PARENTS (CONS (QUOTE :SHORT) (CONS XDOC::SHORT (CONS (QUOTE :LONG) (CONS XDOC::LONG (QUOTE NIL)))))))))))) (WITH-OUTPUT :OFF (EVENT SUMMARY) (PROGN (TABLE XDOC (QUOTE DOC) (CONS (QUOTE ((:NAME . CUTIL::SYMBOL-<-FOO-LIST) (:BASE-PKG . CUTIL::ACL2-PKG-WITNESS) (:PARENTS UNDOCUMENTED) (:SHORT . "@(call SYMBOL-<-FOO-LIST) maps @(see ACL2::SYMBOL-<) across a list.") (:LONG . "<p>This is an ordinary @(see defprojection).</p>

<h3>Definitions and Theorems</h3>@(def |CUTIL|::|SYMBOL-<-FOO-LIST-EXEC|)
@(def |CUTIL|::|SYMBOL-<-FOO-LIST|)
@(def |CUTIL|::|SYMBOL-<-FOO-LIST-WHEN-NOT-CONSP|)
@(def |CUTIL|::|SYMBOL-<-FOO-LIST-OF-CONS|)
@(def |CUTIL|::|TRUE-LISTP-OF-SYMBOL-<-FOO-LIST|)
@(def |CUTIL|::|LEN-OF-SYMBOL-<-FOO-LIST|)
@(def |CUTIL|::|CONSP-OF-SYMBOL-<-FOO-LIST|)
@(def |CUTIL|::|CAR-OF-SYMBOL-<-FOO-LIST|)
@(def |CUTIL|::|CDR-OF-SYMBOL-<-FOO-LIST|)
@(def |CUTIL|::|SYMBOL-<-FOO-LIST-UNDER-IFF|)
@(def |CUTIL|::|SYMBOL-<-FOO-LIST-OF-LIST-FIX|)
@(def |CUTIL|::|SYMBOL-<-FOO-LIST-OF-APPEND|)
@(def |CUTIL|::|SYMBOL-<-FOO-LIST-OF-REV|)
@(def |CUTIL|::|SYMBOL-<-FOO-LIST-OF-REVAPPEND|)
@(def |CUTIL|::|NTHCDR-OF-SYMBOL-<-FOO-LIST|)
@(def |CUTIL|::|MEMBER-EQUAL-OF-SYMBOL-<-IN-SYMBOL-<-FOO-LIST-WHEN-MEMBER-EQUAL|)
@(def |CUTIL|::|SUBSETP-EQUAL-OF-SYMBOL-<-FOO-LISTS-WHEN-SUBSETP-EQUAL|)
@(def |CUTIL|::|SYMBOL-<-FOO-LIST-EXEC-REMOVAL|)") (:FROM . "[books]/cutil/defprojection-tests.lisp"))) (XDOC::GET-XDOC-TABLE WORLD))) (VALUE-TRIPLE (QUOTE (DEFXDOC CUTIL::SYMBOL-<-FOO-LIST)))))) (VALUE-TRIPLE (QUOTE CUTIL::SYMBOL-<-FOO-LIST))))) (23 RECORD-EXPANSION (CUTIL::DEFPROJECTION CUTIL::SYMBOL-<-BAR-LIST (CUTIL::X) (SYMBOL-< (QUOTE CUTIL::BAR) CUTIL::X) :GUARD (SYMBOL-LISTP CUTIL::X)) (WITH-OUTPUT :STACK :PUSH :OFF :ALL :ON ERROR (PROGN (TABLE INTRO-TABLE :MARK (QUOTE CUTIL::SYMBOL-<-BAR-LIST)) (RECORD-EXPANSION (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (LOGIC) (DEFUND CUTIL::SYMBOL-<-BAR-LIST-EXEC (CUTIL::X CUTIL::ACC) (DECLARE (XARGS :GUARD (SYMBOL-LISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (IF (CONSP CUTIL::X) (CUTIL::SYMBOL-<-BAR-LIST-EXEC (CDR CUTIL::X) (CONS (SYMBOL-< (QUOTE CUTIL::BAR) (CAR CUTIL::X)) CUTIL::ACC)) CUTIL::ACC)) (DEFUND CUTIL::SYMBOL-<-BAR-LIST (CUTIL::X) (DECLARE (XARGS :GUARD (SYMBOL-LISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (MBE :LOGIC (IF (CONSP CUTIL::X) (CONS (SYMBOL-< (QUOTE CUTIL::BAR) (CAR CUTIL::X)) (CUTIL::SYMBOL-<-BAR-LIST (CDR CUTIL::X))) NIL) :EXEC (REVERSE (CUTIL::SYMBOL-<-BAR-LIST-EXEC CUTIL::X NIL)))) (SET-INHIBIT-WARNINGS "disable") (LOCAL (MAKE-EVENT (IF (CUTIL::IS-THEOREM-P (QUOTE CUTIL::SYMBOL-<-BAR-LIST-NIL-PRESERVINGP-LEMMA) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (DEFTHM CUTIL::SYMBOL-<-BAR-LIST-NIL-PRESERVINGP-LEMMA (OR (EQUAL (ALISTP CUTIL::X) T) (EQUAL (ALISTP CUTIL::X) NIL)) :RULE-CLASSES :TYPE-PRESCRIPTION :HINTS (("Goal" :IN-THEORY (QUOTE ((:TYPE-PRESCRIPTION ALISTP))))))))))) (DEFTHM CUTIL::SYMBOL-<-BAR-LIST-WHEN-NOT-CONSP (IMPLIES (NOT (CONSP CUTIL::X)) (EQUAL (CUTIL::SYMBOL-<-BAR-LIST CUTIL::X) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-BAR-LIST)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SYMBOL-<-BAR-LIST-OF-CONS (EQUAL (CUTIL::SYMBOL-<-BAR-LIST (CONS CUTIL::A CUTIL::X)) (CONS (SYMBOL-< (QUOTE CUTIL::BAR) CUTIL::A) (CUTIL::SYMBOL-<-BAR-LIST CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-BAR-LIST)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::TRUE-LISTP-OF-SYMBOL-<-BAR-LIST (EQUAL (TRUE-LISTP (CUTIL::SYMBOL-<-BAR-LIST CUTIL::X)) T) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-BAR-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-BAR-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::LEN-OF-SYMBOL-<-BAR-LIST (EQUAL (LEN (CUTIL::SYMBOL-<-BAR-LIST CUTIL::X)) (LEN CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-BAR-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-BAR-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CONSP-OF-SYMBOL-<-BAR-LIST (EQUAL (CONSP (CUTIL::SYMBOL-<-BAR-LIST CUTIL::X)) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-BAR-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-BAR-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CAR-OF-SYMBOL-<-BAR-LIST (EQUAL (CAR (CUTIL::SYMBOL-<-BAR-LIST CUTIL::X)) (IF (CONSP CUTIL::X) (SYMBOL-< (QUOTE CUTIL::BAR) (CAR CUTIL::X)) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-BAR-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-BAR-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CDR-OF-SYMBOL-<-BAR-LIST (EQUAL (CDR (CUTIL::SYMBOL-<-BAR-LIST CUTIL::X)) (CUTIL::SYMBOL-<-BAR-LIST (CDR CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-BAR-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-BAR-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SYMBOL-<-BAR-LIST-UNDER-IFF (IFF (CUTIL::SYMBOL-<-BAR-LIST CUTIL::X) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-BAR-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-BAR-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SYMBOL-<-BAR-LIST-OF-LIST-FIX (EQUAL (CUTIL::SYMBOL-<-BAR-LIST (LIST-FIX CUTIL::X)) (CUTIL::SYMBOL-<-BAR-LIST CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-BAR-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-BAR-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SYMBOL-<-BAR-LIST-OF-APPEND (EQUAL (CUTIL::SYMBOL-<-BAR-LIST (APPEND CUTIL::X CUTIL::Y)) (APPEND (CUTIL::SYMBOL-<-BAR-LIST CUTIL::X) (CUTIL::SYMBOL-<-BAR-LIST CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-BAR-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-BAR-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SYMBOL-<-BAR-LIST-OF-REV (EQUAL (CUTIL::SYMBOL-<-BAR-LIST (REV CUTIL::X)) (REV (CUTIL::SYMBOL-<-BAR-LIST CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-BAR-LIST-OF-APPEND CUTIL::SYMBOL-<-BAR-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-BAR-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SYMBOL-<-BAR-LIST-OF-REVAPPEND (EQUAL (CUTIL::SYMBOL-<-BAR-LIST (REVAPPEND CUTIL::X CUTIL::Y)) (REVAPPEND (CUTIL::SYMBOL-<-BAR-LIST CUTIL::X) (CUTIL::SYMBOL-<-BAR-LIST CUTIL::Y))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-BAR-LIST-OF-APPEND CUTIL::SYMBOL-<-BAR-LIST-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::NTHCDR-OF-SYMBOL-<-BAR-LIST (EQUAL (NTHCDR CUTIL::N (CUTIL::SYMBOL-<-BAR-LIST CUTIL::X)) (CUTIL::SYMBOL-<-BAR-LIST (NTHCDR CUTIL::N CUTIL::X))) :HINTS (("Goal" :INDUCT (NTHCDR CUTIL::N CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (NTHCDR CUTIL::SYMBOL-<-BAR-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-BAR-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MEMBER-EQUAL-OF-SYMBOL-<-IN-SYMBOL-<-BAR-LIST-WHEN-MEMBER-EQUAL (IMPLIES (MEMBER-EQUAL CUTIL::A (DOUBLE-REWRITE CUTIL::X)) (MEMBER-EQUAL (SYMBOL-< (QUOTE CUTIL::BAR) CUTIL::A) (CUTIL::SYMBOL-<-BAR-LIST CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (MEMBER-EQUAL CUTIL::SYMBOL-<-BAR-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-BAR-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SUBSETP-EQUAL-OF-SYMBOL-<-BAR-LISTS-WHEN-SUBSETP-EQUAL (IMPLIES (SUBSETP-EQUAL (DOUBLE-REWRITE CUTIL::X) (DOUBLE-REWRITE CUTIL::Y)) (SUBSETP-EQUAL (CUTIL::SYMBOL-<-BAR-LIST CUTIL::X) (CUTIL::SYMBOL-<-BAR-LIST CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (SUBSETP-EQUAL CUTIL::MEMBER-EQUAL-OF-SYMBOL-<-IN-SYMBOL-<-BAR-LIST-WHEN-MEMBER-EQUAL CUTIL::SYMBOL-<-BAR-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-BAR-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SYMBOL-<-BAR-LIST-EXEC-REMOVAL (EQUAL (CUTIL::SYMBOL-<-BAR-LIST-EXEC CUTIL::X CUTIL::ACC) (REVAPPEND (CUTIL::SYMBOL-<-BAR-LIST CUTIL::X) CUTIL::ACC)) :HINTS (("Goal" :INDUCT (CUTIL::SYMBOL-<-BAR-LIST-EXEC CUTIL::X CUTIL::ACC) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-BAR-LIST-EXEC CUTIL::SYMBOL-<-BAR-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-BAR-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (VERIFY-GUARDS CUTIL::SYMBOL-<-BAR-LIST-EXEC :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-BAR-LIST-EXEC)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (VERIFY-GUARDS CUTIL::SYMBOL-<-BAR-LIST :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-BAR-LIST CUTIL::SYMBOL-<-BAR-LIST-EXEC-REMOVAL CUTIL::TRUE-LISTP-OF-SYMBOL-<-BAR-LIST REVERSE-REMOVAL REVAPPEND-REMOVAL REV-OF-APPEND REV-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (PROGN (MAKE-EVENT (IF (GLOBAL-VAL (QUOTE INCLUDE-BOOK-PATH) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::SYMBOL-<-BAR-LIST) (QUOTE (DEFUN CUTIL::SYMBOL-<-BAR-LIST (CUTIL::X) (NREVERSE (CUTIL::SYMBOL-<-BAR-LIST-EXEC CUTIL::X NIL)))))))))) (DEFTTAG CUTIL::CUTIL-OPTIMIZE) (NEVER-MEMOIZE CUTIL::SYMBOL-<-BAR-LIST-EXEC) (PROGN! (SET-RAW-MODE T) (DEFUN CUTIL::SYMBOL-<-BAR-LIST (CUTIL::X) (NREVERSE (CUTIL::SYMBOL-<-BAR-LIST-EXEC CUTIL::X NIL)))) (DEFTTAG NIL)) (LOCAL (IN-THEORY (ENABLE CUTIL::SYMBOL-<-BAR-LIST CUTIL::SYMBOL-<-BAR-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-BAR-LIST-OF-CONS))))) (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (LOGIC) (DEFUND CUTIL::SYMBOL-<-BAR-LIST-EXEC (CUTIL::X CUTIL::ACC) (DECLARE (XARGS :GUARD (SYMBOL-LISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (IF (CONSP CUTIL::X) (CUTIL::SYMBOL-<-BAR-LIST-EXEC (CDR CUTIL::X) (CONS (SYMBOL-< (QUOTE CUTIL::BAR) (CAR CUTIL::X)) CUTIL::ACC)) CUTIL::ACC)) (DEFUND CUTIL::SYMBOL-<-BAR-LIST (CUTIL::X) (DECLARE (XARGS :GUARD (SYMBOL-LISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (MBE :LOGIC (IF (CONSP CUTIL::X) (CONS (SYMBOL-< (QUOTE CUTIL::BAR) (CAR CUTIL::X)) (CUTIL::SYMBOL-<-BAR-LIST (CDR CUTIL::X))) NIL) :EXEC (REVERSE (CUTIL::SYMBOL-<-BAR-LIST-EXEC CUTIL::X NIL)))) (SET-INHIBIT-WARNINGS "disable") (RECORD-EXPANSION (LOCAL (MAKE-EVENT (IF (CUTIL::IS-THEOREM-P (QUOTE CUTIL::SYMBOL-<-BAR-LIST-NIL-PRESERVINGP-LEMMA) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (DEFTHM CUTIL::SYMBOL-<-BAR-LIST-NIL-PRESERVINGP-LEMMA (OR (EQUAL (ALISTP CUTIL::X) T) (EQUAL (ALISTP CUTIL::X) NIL)) :RULE-CLASSES :TYPE-PRESCRIPTION :HINTS (("Goal" :IN-THEORY (QUOTE ((:TYPE-PRESCRIPTION ALISTP))))))))))) (LOCAL (VALUE-TRIPLE :ELIDED))) (DEFTHM CUTIL::SYMBOL-<-BAR-LIST-WHEN-NOT-CONSP (IMPLIES (NOT (CONSP CUTIL::X)) (EQUAL (CUTIL::SYMBOL-<-BAR-LIST CUTIL::X) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-BAR-LIST)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SYMBOL-<-BAR-LIST-OF-CONS (EQUAL (CUTIL::SYMBOL-<-BAR-LIST (CONS CUTIL::A CUTIL::X)) (CONS (SYMBOL-< (QUOTE CUTIL::BAR) CUTIL::A) (CUTIL::SYMBOL-<-BAR-LIST CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-BAR-LIST)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::TRUE-LISTP-OF-SYMBOL-<-BAR-LIST (EQUAL (TRUE-LISTP (CUTIL::SYMBOL-<-BAR-LIST CUTIL::X)) T) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-BAR-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-BAR-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::LEN-OF-SYMBOL-<-BAR-LIST (EQUAL (LEN (CUTIL::SYMBOL-<-BAR-LIST CUTIL::X)) (LEN CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-BAR-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-BAR-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CONSP-OF-SYMBOL-<-BAR-LIST (EQUAL (CONSP (CUTIL::SYMBOL-<-BAR-LIST CUTIL::X)) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-BAR-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-BAR-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CAR-OF-SYMBOL-<-BAR-LIST (EQUAL (CAR (CUTIL::SYMBOL-<-BAR-LIST CUTIL::X)) (IF (CONSP CUTIL::X) (SYMBOL-< (QUOTE CUTIL::BAR) (CAR CUTIL::X)) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-BAR-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-BAR-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CDR-OF-SYMBOL-<-BAR-LIST (EQUAL (CDR (CUTIL::SYMBOL-<-BAR-LIST CUTIL::X)) (CUTIL::SYMBOL-<-BAR-LIST (CDR CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-BAR-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-BAR-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SYMBOL-<-BAR-LIST-UNDER-IFF (IFF (CUTIL::SYMBOL-<-BAR-LIST CUTIL::X) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-BAR-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-BAR-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SYMBOL-<-BAR-LIST-OF-LIST-FIX (EQUAL (CUTIL::SYMBOL-<-BAR-LIST (LIST-FIX CUTIL::X)) (CUTIL::SYMBOL-<-BAR-LIST CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-BAR-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-BAR-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SYMBOL-<-BAR-LIST-OF-APPEND (EQUAL (CUTIL::SYMBOL-<-BAR-LIST (APPEND CUTIL::X CUTIL::Y)) (APPEND (CUTIL::SYMBOL-<-BAR-LIST CUTIL::X) (CUTIL::SYMBOL-<-BAR-LIST CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-BAR-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-BAR-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SYMBOL-<-BAR-LIST-OF-REV (EQUAL (CUTIL::SYMBOL-<-BAR-LIST (REV CUTIL::X)) (REV (CUTIL::SYMBOL-<-BAR-LIST CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-BAR-LIST-OF-APPEND CUTIL::SYMBOL-<-BAR-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-BAR-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SYMBOL-<-BAR-LIST-OF-REVAPPEND (EQUAL (CUTIL::SYMBOL-<-BAR-LIST (REVAPPEND CUTIL::X CUTIL::Y)) (REVAPPEND (CUTIL::SYMBOL-<-BAR-LIST CUTIL::X) (CUTIL::SYMBOL-<-BAR-LIST CUTIL::Y))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-BAR-LIST-OF-APPEND CUTIL::SYMBOL-<-BAR-LIST-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::NTHCDR-OF-SYMBOL-<-BAR-LIST (EQUAL (NTHCDR CUTIL::N (CUTIL::SYMBOL-<-BAR-LIST CUTIL::X)) (CUTIL::SYMBOL-<-BAR-LIST (NTHCDR CUTIL::N CUTIL::X))) :HINTS (("Goal" :INDUCT (NTHCDR CUTIL::N CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (NTHCDR CUTIL::SYMBOL-<-BAR-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-BAR-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MEMBER-EQUAL-OF-SYMBOL-<-IN-SYMBOL-<-BAR-LIST-WHEN-MEMBER-EQUAL (IMPLIES (MEMBER-EQUAL CUTIL::A (DOUBLE-REWRITE CUTIL::X)) (MEMBER-EQUAL (SYMBOL-< (QUOTE CUTIL::BAR) CUTIL::A) (CUTIL::SYMBOL-<-BAR-LIST CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (MEMBER-EQUAL CUTIL::SYMBOL-<-BAR-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-BAR-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SUBSETP-EQUAL-OF-SYMBOL-<-BAR-LISTS-WHEN-SUBSETP-EQUAL (IMPLIES (SUBSETP-EQUAL (DOUBLE-REWRITE CUTIL::X) (DOUBLE-REWRITE CUTIL::Y)) (SUBSETP-EQUAL (CUTIL::SYMBOL-<-BAR-LIST CUTIL::X) (CUTIL::SYMBOL-<-BAR-LIST CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (SUBSETP-EQUAL CUTIL::MEMBER-EQUAL-OF-SYMBOL-<-IN-SYMBOL-<-BAR-LIST-WHEN-MEMBER-EQUAL CUTIL::SYMBOL-<-BAR-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-BAR-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SYMBOL-<-BAR-LIST-EXEC-REMOVAL (EQUAL (CUTIL::SYMBOL-<-BAR-LIST-EXEC CUTIL::X CUTIL::ACC) (REVAPPEND (CUTIL::SYMBOL-<-BAR-LIST CUTIL::X) CUTIL::ACC)) :HINTS (("Goal" :INDUCT (CUTIL::SYMBOL-<-BAR-LIST-EXEC CUTIL::X CUTIL::ACC) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-BAR-LIST-EXEC CUTIL::SYMBOL-<-BAR-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-BAR-LIST-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (VERIFY-GUARDS CUTIL::SYMBOL-<-BAR-LIST-EXEC :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-BAR-LIST-EXEC)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (VERIFY-GUARDS CUTIL::SYMBOL-<-BAR-LIST :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::SYMBOL-<-BAR-LIST CUTIL::SYMBOL-<-BAR-LIST-EXEC-REMOVAL CUTIL::TRUE-LISTP-OF-SYMBOL-<-BAR-LIST REVERSE-REMOVAL REVAPPEND-REMOVAL REV-OF-APPEND REV-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (RECORD-EXPANSION (PROGN (MAKE-EVENT (IF (GLOBAL-VAL (QUOTE INCLUDE-BOOK-PATH) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::SYMBOL-<-BAR-LIST) (QUOTE (DEFUN CUTIL::SYMBOL-<-BAR-LIST (CUTIL::X) (NREVERSE (CUTIL::SYMBOL-<-BAR-LIST-EXEC CUTIL::X NIL)))))))))) (DEFTTAG CUTIL::CUTIL-OPTIMIZE) (NEVER-MEMOIZE CUTIL::SYMBOL-<-BAR-LIST-EXEC) (PROGN! (SET-RAW-MODE T) (DEFUN CUTIL::SYMBOL-<-BAR-LIST (CUTIL::X) (NREVERSE (CUTIL::SYMBOL-<-BAR-LIST-EXEC CUTIL::X NIL)))) (DEFTTAG NIL)) (PROGN (RECORD-EXPANSION (MAKE-EVENT (IF (GLOBAL-VAL (QUOTE INCLUDE-BOOK-PATH) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::SYMBOL-<-BAR-LIST) (QUOTE (DEFUN CUTIL::SYMBOL-<-BAR-LIST (CUTIL::X) (NREVERSE (CUTIL::SYMBOL-<-BAR-LIST-EXEC CUTIL::X NIL)))))))))) (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::SYMBOL-<-BAR-LIST) (QUOTE (DEFUN CUTIL::SYMBOL-<-BAR-LIST (CUTIL::X) (NREVERSE (CUTIL::SYMBOL-<-BAR-LIST-EXEC CUTIL::X NIL))))))) (DEFTTAG CUTIL::CUTIL-OPTIMIZE) (RECORD-EXPANSION (NEVER-MEMOIZE CUTIL::SYMBOL-<-BAR-LIST-EXEC) (MAKE-EVENT (PROG2$ (NEVER-MEMOIZE-FN (QUOTE CUTIL::SYMBOL-<-BAR-LIST-EXEC)) (QUOTE (VALUE-TRIPLE :INVISIBLE))) :CHECK-EXPANSION (VALUE-TRIPLE :INVISIBLE))) (PROGN! (SET-RAW-MODE T) (DEFUN CUTIL::SYMBOL-<-BAR-LIST (CUTIL::X) (NREVERSE (CUTIL::SYMBOL-<-BAR-LIST-EXEC CUTIL::X NIL)))) (DEFTTAG NIL))) (LOCAL (IN-THEORY (ENABLE CUTIL::SYMBOL-<-BAR-LIST CUTIL::SYMBOL-<-BAR-LIST-WHEN-NOT-CONSP CUTIL::SYMBOL-<-BAR-LIST-OF-CONS)))))) (RECORD-EXPANSION (MAKE-EVENT (LET* ((XDOC::NAME (QUOTE CUTIL::SYMBOL-<-BAR-LIST)) (XDOC::PARENTS (QUOTE (UNDOCUMENTED))) (XDOC::SHORT (QUOTE "@(call SYMBOL-<-BAR-LIST) maps @(see ACL2::SYMBOL-<) across a list.")) (XDOC::EXTENSION (QUOTE NIL)) (XDOC::WRLD (W STATE)) (XDOC::TRIPS (REVERSED-WORLD-SINCE-EVENT XDOC::WRLD (QUOTE (TABLE INTRO-TABLE :MARK (QUOTE CUTIL::SYMBOL-<-BAR-LIST))) NIL)) (XDOC::INFO (REVERSE (NEW-FORMULA-INFO XDOC::TRIPS XDOC::WRLD NIL))) (XDOC::AUTODOC (XDOC::FORMULA-INFO-TO-DEFS (NOT XDOC::EXTENSION) XDOC::INFO)) (XDOC::LONG (CONCATENATE (QUOTE STRING) (QUOTE "<p>This is an ordinary @(see defprojection).</p>") (COERCE (LIST #\Newline #\Newline) (QUOTE STRING)) XDOC::AUTODOC))) (IF XDOC::EXTENSION (CONS (QUOTE XDOC-EXTEND) (CONS XDOC::EXTENSION (CONS XDOC::LONG (QUOTE NIL)))) (CONS (QUOTE DEFXDOC) (CONS XDOC::NAME (CONS (QUOTE :PARENTS) (CONS XDOC::PARENTS (CONS (QUOTE :SHORT) (CONS XDOC::SHORT (CONS (QUOTE :LONG) (CONS XDOC::LONG (QUOTE NIL)))))))))))) (WITH-OUTPUT :OFF (EVENT SUMMARY) (PROGN (TABLE XDOC (QUOTE DOC) (CONS (QUOTE ((:NAME . CUTIL::SYMBOL-<-BAR-LIST) (:BASE-PKG . CUTIL::ACL2-PKG-WITNESS) (:PARENTS UNDOCUMENTED) (:SHORT . "@(call SYMBOL-<-BAR-LIST) maps @(see ACL2::SYMBOL-<) across a list.") (:LONG . "<p>This is an ordinary @(see defprojection).</p>

<h3>Definitions and Theorems</h3>@(def |CUTIL|::|SYMBOL-<-BAR-LIST-EXEC|)
@(def |CUTIL|::|SYMBOL-<-BAR-LIST|)
@(def |CUTIL|::|SYMBOL-<-BAR-LIST-WHEN-NOT-CONSP|)
@(def |CUTIL|::|SYMBOL-<-BAR-LIST-OF-CONS|)
@(def |CUTIL|::|TRUE-LISTP-OF-SYMBOL-<-BAR-LIST|)
@(def |CUTIL|::|LEN-OF-SYMBOL-<-BAR-LIST|)
@(def |CUTIL|::|CONSP-OF-SYMBOL-<-BAR-LIST|)
@(def |CUTIL|::|CAR-OF-SYMBOL-<-BAR-LIST|)
@(def |CUTIL|::|CDR-OF-SYMBOL-<-BAR-LIST|)
@(def |CUTIL|::|SYMBOL-<-BAR-LIST-UNDER-IFF|)
@(def |CUTIL|::|SYMBOL-<-BAR-LIST-OF-LIST-FIX|)
@(def |CUTIL|::|SYMBOL-<-BAR-LIST-OF-APPEND|)
@(def |CUTIL|::|SYMBOL-<-BAR-LIST-OF-REV|)
@(def |CUTIL|::|SYMBOL-<-BAR-LIST-OF-REVAPPEND|)
@(def |CUTIL|::|NTHCDR-OF-SYMBOL-<-BAR-LIST|)
@(def |CUTIL|::|MEMBER-EQUAL-OF-SYMBOL-<-IN-SYMBOL-<-BAR-LIST-WHEN-MEMBER-EQUAL|)
@(def |CUTIL|::|SUBSETP-EQUAL-OF-SYMBOL-<-BAR-LISTS-WHEN-SUBSETP-EQUAL|)
@(def |CUTIL|::|SYMBOL-<-BAR-LIST-EXEC-REMOVAL|)") (:FROM . "[books]/cutil/defprojection-tests.lisp"))) (XDOC::GET-XDOC-TABLE WORLD))) (VALUE-TRIPLE (QUOTE (DEFXDOC CUTIL::SYMBOL-<-BAR-LIST)))))) (VALUE-TRIPLE (QUOTE CUTIL::SYMBOL-<-BAR-LIST))))) (25 RECORD-EXPANSION (CUTIL::DEFPROJECTION CUTIL::MY-STRIP-CARS (CUTIL::X) (CAR CUTIL::X) :NIL-PRESERVINGP T :GUARD (ALISTP CUTIL::X)) (WITH-OUTPUT :STACK :PUSH :OFF :ALL :ON ERROR (PROGN (TABLE INTRO-TABLE :MARK (QUOTE CUTIL::MY-STRIP-CARS)) (RECORD-EXPANSION (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (LOGIC) (DEFUND CUTIL::MY-STRIP-CARS-EXEC (CUTIL::X CUTIL::ACC) (DECLARE (XARGS :GUARD (ALISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (IF (CONSP CUTIL::X) (CUTIL::MY-STRIP-CARS-EXEC (CDR CUTIL::X) (CONS (CAR (CAR CUTIL::X)) CUTIL::ACC)) CUTIL::ACC)) (DEFUND CUTIL::MY-STRIP-CARS (CUTIL::X) (DECLARE (XARGS :GUARD (ALISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (MBE :LOGIC (IF (CONSP CUTIL::X) (CONS (CAR (CAR CUTIL::X)) (CUTIL::MY-STRIP-CARS (CDR CUTIL::X))) NIL) :EXEC (REVERSE (CUTIL::MY-STRIP-CARS-EXEC CUTIL::X NIL)))) (SET-INHIBIT-WARNINGS "disable") (LOCAL (CUTIL::MAYBE-DEFTHM-AS-REWRITE CUTIL::MY-STRIP-CARS-NIL-PRESERVINGP-LEMMA (EQUAL (CAR (QUOTE NIL)) NIL))) (LOCAL (MAKE-EVENT (IF (CUTIL::IS-THEOREM-P (QUOTE CUTIL::MY-STRIP-CARS-NIL-PRESERVINGP-LEMMA) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (DEFTHM CUTIL::MY-STRIP-CARS-NIL-PRESERVINGP-LEMMA (OR (EQUAL (ALISTP CUTIL::X) T) (EQUAL (ALISTP CUTIL::X) NIL)) :RULE-CLASSES :TYPE-PRESCRIPTION :HINTS (("Goal" :IN-THEORY (QUOTE ((:TYPE-PRESCRIPTION ALISTP))))))))))) (DEFTHM CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP (IMPLIES (NOT (CONSP CUTIL::X)) (EQUAL (CUTIL::MY-STRIP-CARS CUTIL::X) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MY-STRIP-CARS-OF-CONS (EQUAL (CUTIL::MY-STRIP-CARS (CONS CUTIL::A CUTIL::X)) (CONS (CAR CUTIL::A) (CUTIL::MY-STRIP-CARS CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::TRUE-LISTP-OF-MY-STRIP-CARS (EQUAL (TRUE-LISTP (CUTIL::MY-STRIP-CARS CUTIL::X)) T) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::LEN-OF-MY-STRIP-CARS (EQUAL (LEN (CUTIL::MY-STRIP-CARS CUTIL::X)) (LEN CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CONSP-OF-MY-STRIP-CARS (EQUAL (CONSP (CUTIL::MY-STRIP-CARS CUTIL::X)) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CAR-OF-MY-STRIP-CARS (EQUAL (CAR (CUTIL::MY-STRIP-CARS CUTIL::X)) (CAR (CAR CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS-OF-CONS CUTIL::MY-STRIP-CARS-NIL-PRESERVINGP-LEMMA DEFAULT-CAR)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CDR-OF-MY-STRIP-CARS (EQUAL (CDR (CUTIL::MY-STRIP-CARS CUTIL::X)) (CUTIL::MY-STRIP-CARS (CDR CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MY-STRIP-CARS-UNDER-IFF (IFF (CUTIL::MY-STRIP-CARS CUTIL::X) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MY-STRIP-CARS-OF-LIST-FIX (EQUAL (CUTIL::MY-STRIP-CARS (LIST-FIX CUTIL::X)) (CUTIL::MY-STRIP-CARS CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MY-STRIP-CARS-OF-APPEND (EQUAL (CUTIL::MY-STRIP-CARS (APPEND CUTIL::X CUTIL::Y)) (APPEND (CUTIL::MY-STRIP-CARS CUTIL::X) (CUTIL::MY-STRIP-CARS CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MY-STRIP-CARS-OF-REV (EQUAL (CUTIL::MY-STRIP-CARS (REV CUTIL::X)) (REV (CUTIL::MY-STRIP-CARS CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS-OF-APPEND CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MY-STRIP-CARS-OF-REVAPPEND (EQUAL (CUTIL::MY-STRIP-CARS (REVAPPEND CUTIL::X CUTIL::Y)) (REVAPPEND (CUTIL::MY-STRIP-CARS CUTIL::X) (CUTIL::MY-STRIP-CARS CUTIL::Y))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS-OF-APPEND CUTIL::MY-STRIP-CARS-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::TAKE-OF-MY-STRIP-CARS (EQUAL (TAKE CUTIL::N (CUTIL::MY-STRIP-CARS CUTIL::X)) (CUTIL::MY-STRIP-CARS (TAKE CUTIL::N CUTIL::X))) :HINTS (("Goal" :INDUCT (TAKE CUTIL::N CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (TAKE-REDEFINITION CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS-OF-CONS CUTIL::MY-STRIP-CARS-NIL-PRESERVINGP-LEMMA DEFAULT-CAR)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::NTHCDR-OF-MY-STRIP-CARS (EQUAL (NTHCDR CUTIL::N (CUTIL::MY-STRIP-CARS CUTIL::X)) (CUTIL::MY-STRIP-CARS (NTHCDR CUTIL::N CUTIL::X))) :HINTS (("Goal" :INDUCT (NTHCDR CUTIL::N CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (NTHCDR CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MEMBER-EQUAL-OF-CAR-IN-MY-STRIP-CARS-WHEN-MEMBER-EQUAL (IMPLIES (MEMBER-EQUAL CUTIL::A (DOUBLE-REWRITE CUTIL::X)) (MEMBER-EQUAL (CAR CUTIL::A) (CUTIL::MY-STRIP-CARS CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (MEMBER-EQUAL CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SUBSETP-EQUAL-OF-MY-STRIP-CARSS-WHEN-SUBSETP-EQUAL (IMPLIES (SUBSETP-EQUAL (DOUBLE-REWRITE CUTIL::X) (DOUBLE-REWRITE CUTIL::Y)) (SUBSETP-EQUAL (CUTIL::MY-STRIP-CARS CUTIL::X) (CUTIL::MY-STRIP-CARS CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (SUBSETP-EQUAL CUTIL::MEMBER-EQUAL-OF-CAR-IN-MY-STRIP-CARS-WHEN-MEMBER-EQUAL CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::NTH-OF-MY-STRIP-CARS (EQUAL (NTH CUTIL::N (CUTIL::MY-STRIP-CARS CUTIL::X)) (CAR (NTH CUTIL::N CUTIL::X))) :HINTS (("Goal" :INDUCT (NTH CUTIL::N CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (NTH CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS-OF-CONS CUTIL::MY-STRIP-CARS-NIL-PRESERVINGP-LEMMA DEFAULT-CAR)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MY-STRIP-CARS-EXEC-REMOVAL (EQUAL (CUTIL::MY-STRIP-CARS-EXEC CUTIL::X CUTIL::ACC) (REVAPPEND (CUTIL::MY-STRIP-CARS CUTIL::X) CUTIL::ACC)) :HINTS (("Goal" :INDUCT (CUTIL::MY-STRIP-CARS-EXEC CUTIL::X CUTIL::ACC) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS-EXEC CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (VERIFY-GUARDS CUTIL::MY-STRIP-CARS-EXEC :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS-EXEC)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (VERIFY-GUARDS CUTIL::MY-STRIP-CARS :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS CUTIL::MY-STRIP-CARS-EXEC-REMOVAL CUTIL::TRUE-LISTP-OF-MY-STRIP-CARS REVERSE-REMOVAL REVAPPEND-REMOVAL REV-OF-APPEND REV-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (PROGN (MAKE-EVENT (IF (GLOBAL-VAL (QUOTE INCLUDE-BOOK-PATH) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::MY-STRIP-CARS) (QUOTE (DEFUN CUTIL::MY-STRIP-CARS (CUTIL::X) (NREVERSE (CUTIL::MY-STRIP-CARS-EXEC CUTIL::X NIL)))))))))) (DEFTTAG CUTIL::CUTIL-OPTIMIZE) (NEVER-MEMOIZE CUTIL::MY-STRIP-CARS-EXEC) (PROGN! (SET-RAW-MODE T) (DEFUN CUTIL::MY-STRIP-CARS (CUTIL::X) (NREVERSE (CUTIL::MY-STRIP-CARS-EXEC CUTIL::X NIL)))) (DEFTTAG NIL)) (LOCAL (IN-THEORY (ENABLE CUTIL::MY-STRIP-CARS CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS-OF-CONS))))) (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (LOGIC) (DEFUND CUTIL::MY-STRIP-CARS-EXEC (CUTIL::X CUTIL::ACC) (DECLARE (XARGS :GUARD (ALISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (IF (CONSP CUTIL::X) (CUTIL::MY-STRIP-CARS-EXEC (CDR CUTIL::X) (CONS (CAR (CAR CUTIL::X)) CUTIL::ACC)) CUTIL::ACC)) (DEFUND CUTIL::MY-STRIP-CARS (CUTIL::X) (DECLARE (XARGS :GUARD (ALISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (MBE :LOGIC (IF (CONSP CUTIL::X) (CONS (CAR (CAR CUTIL::X)) (CUTIL::MY-STRIP-CARS (CDR CUTIL::X))) NIL) :EXEC (REVERSE (CUTIL::MY-STRIP-CARS-EXEC CUTIL::X NIL)))) (SET-INHIBIT-WARNINGS "disable") (RECORD-EXPANSION (LOCAL (CUTIL::MAYBE-DEFTHM-AS-REWRITE CUTIL::MY-STRIP-CARS-NIL-PRESERVINGP-LEMMA (EQUAL (CAR (QUOTE NIL)) NIL))) (LOCAL (VALUE-TRIPLE :ELIDED))) (RECORD-EXPANSION (LOCAL (MAKE-EVENT (IF (CUTIL::IS-THEOREM-P (QUOTE CUTIL::MY-STRIP-CARS-NIL-PRESERVINGP-LEMMA) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (DEFTHM CUTIL::MY-STRIP-CARS-NIL-PRESERVINGP-LEMMA (OR (EQUAL (ALISTP CUTIL::X) T) (EQUAL (ALISTP CUTIL::X) NIL)) :RULE-CLASSES :TYPE-PRESCRIPTION :HINTS (("Goal" :IN-THEORY (QUOTE ((:TYPE-PRESCRIPTION ALISTP))))))))))) (LOCAL (VALUE-TRIPLE :ELIDED))) (DEFTHM CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP (IMPLIES (NOT (CONSP CUTIL::X)) (EQUAL (CUTIL::MY-STRIP-CARS CUTIL::X) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MY-STRIP-CARS-OF-CONS (EQUAL (CUTIL::MY-STRIP-CARS (CONS CUTIL::A CUTIL::X)) (CONS (CAR CUTIL::A) (CUTIL::MY-STRIP-CARS CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::TRUE-LISTP-OF-MY-STRIP-CARS (EQUAL (TRUE-LISTP (CUTIL::MY-STRIP-CARS CUTIL::X)) T) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::LEN-OF-MY-STRIP-CARS (EQUAL (LEN (CUTIL::MY-STRIP-CARS CUTIL::X)) (LEN CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CONSP-OF-MY-STRIP-CARS (EQUAL (CONSP (CUTIL::MY-STRIP-CARS CUTIL::X)) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CAR-OF-MY-STRIP-CARS (EQUAL (CAR (CUTIL::MY-STRIP-CARS CUTIL::X)) (CAR (CAR CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS-OF-CONS CUTIL::MY-STRIP-CARS-NIL-PRESERVINGP-LEMMA DEFAULT-CAR)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CDR-OF-MY-STRIP-CARS (EQUAL (CDR (CUTIL::MY-STRIP-CARS CUTIL::X)) (CUTIL::MY-STRIP-CARS (CDR CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MY-STRIP-CARS-UNDER-IFF (IFF (CUTIL::MY-STRIP-CARS CUTIL::X) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MY-STRIP-CARS-OF-LIST-FIX (EQUAL (CUTIL::MY-STRIP-CARS (LIST-FIX CUTIL::X)) (CUTIL::MY-STRIP-CARS CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MY-STRIP-CARS-OF-APPEND (EQUAL (CUTIL::MY-STRIP-CARS (APPEND CUTIL::X CUTIL::Y)) (APPEND (CUTIL::MY-STRIP-CARS CUTIL::X) (CUTIL::MY-STRIP-CARS CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MY-STRIP-CARS-OF-REV (EQUAL (CUTIL::MY-STRIP-CARS (REV CUTIL::X)) (REV (CUTIL::MY-STRIP-CARS CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS-OF-APPEND CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MY-STRIP-CARS-OF-REVAPPEND (EQUAL (CUTIL::MY-STRIP-CARS (REVAPPEND CUTIL::X CUTIL::Y)) (REVAPPEND (CUTIL::MY-STRIP-CARS CUTIL::X) (CUTIL::MY-STRIP-CARS CUTIL::Y))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS-OF-APPEND CUTIL::MY-STRIP-CARS-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::TAKE-OF-MY-STRIP-CARS (EQUAL (TAKE CUTIL::N (CUTIL::MY-STRIP-CARS CUTIL::X)) (CUTIL::MY-STRIP-CARS (TAKE CUTIL::N CUTIL::X))) :HINTS (("Goal" :INDUCT (TAKE CUTIL::N CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (TAKE-REDEFINITION CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS-OF-CONS CUTIL::MY-STRIP-CARS-NIL-PRESERVINGP-LEMMA DEFAULT-CAR)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::NTHCDR-OF-MY-STRIP-CARS (EQUAL (NTHCDR CUTIL::N (CUTIL::MY-STRIP-CARS CUTIL::X)) (CUTIL::MY-STRIP-CARS (NTHCDR CUTIL::N CUTIL::X))) :HINTS (("Goal" :INDUCT (NTHCDR CUTIL::N CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (NTHCDR CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MEMBER-EQUAL-OF-CAR-IN-MY-STRIP-CARS-WHEN-MEMBER-EQUAL (IMPLIES (MEMBER-EQUAL CUTIL::A (DOUBLE-REWRITE CUTIL::X)) (MEMBER-EQUAL (CAR CUTIL::A) (CUTIL::MY-STRIP-CARS CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (MEMBER-EQUAL CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SUBSETP-EQUAL-OF-MY-STRIP-CARSS-WHEN-SUBSETP-EQUAL (IMPLIES (SUBSETP-EQUAL (DOUBLE-REWRITE CUTIL::X) (DOUBLE-REWRITE CUTIL::Y)) (SUBSETP-EQUAL (CUTIL::MY-STRIP-CARS CUTIL::X) (CUTIL::MY-STRIP-CARS CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (SUBSETP-EQUAL CUTIL::MEMBER-EQUAL-OF-CAR-IN-MY-STRIP-CARS-WHEN-MEMBER-EQUAL CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::NTH-OF-MY-STRIP-CARS (EQUAL (NTH CUTIL::N (CUTIL::MY-STRIP-CARS CUTIL::X)) (CAR (NTH CUTIL::N CUTIL::X))) :HINTS (("Goal" :INDUCT (NTH CUTIL::N CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (NTH CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS-OF-CONS CUTIL::MY-STRIP-CARS-NIL-PRESERVINGP-LEMMA DEFAULT-CAR)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MY-STRIP-CARS-EXEC-REMOVAL (EQUAL (CUTIL::MY-STRIP-CARS-EXEC CUTIL::X CUTIL::ACC) (REVAPPEND (CUTIL::MY-STRIP-CARS CUTIL::X) CUTIL::ACC)) :HINTS (("Goal" :INDUCT (CUTIL::MY-STRIP-CARS-EXEC CUTIL::X CUTIL::ACC) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS-EXEC CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (VERIFY-GUARDS CUTIL::MY-STRIP-CARS-EXEC :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS-EXEC)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (VERIFY-GUARDS CUTIL::MY-STRIP-CARS :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS CUTIL::MY-STRIP-CARS-EXEC-REMOVAL CUTIL::TRUE-LISTP-OF-MY-STRIP-CARS REVERSE-REMOVAL REVAPPEND-REMOVAL REV-OF-APPEND REV-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (RECORD-EXPANSION (PROGN (MAKE-EVENT (IF (GLOBAL-VAL (QUOTE INCLUDE-BOOK-PATH) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::MY-STRIP-CARS) (QUOTE (DEFUN CUTIL::MY-STRIP-CARS (CUTIL::X) (NREVERSE (CUTIL::MY-STRIP-CARS-EXEC CUTIL::X NIL)))))))))) (DEFTTAG CUTIL::CUTIL-OPTIMIZE) (NEVER-MEMOIZE CUTIL::MY-STRIP-CARS-EXEC) (PROGN! (SET-RAW-MODE T) (DEFUN CUTIL::MY-STRIP-CARS (CUTIL::X) (NREVERSE (CUTIL::MY-STRIP-CARS-EXEC CUTIL::X NIL)))) (DEFTTAG NIL)) (PROGN (RECORD-EXPANSION (MAKE-EVENT (IF (GLOBAL-VAL (QUOTE INCLUDE-BOOK-PATH) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::MY-STRIP-CARS) (QUOTE (DEFUN CUTIL::MY-STRIP-CARS (CUTIL::X) (NREVERSE (CUTIL::MY-STRIP-CARS-EXEC CUTIL::X NIL)))))))))) (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::MY-STRIP-CARS) (QUOTE (DEFUN CUTIL::MY-STRIP-CARS (CUTIL::X) (NREVERSE (CUTIL::MY-STRIP-CARS-EXEC CUTIL::X NIL))))))) (DEFTTAG CUTIL::CUTIL-OPTIMIZE) (RECORD-EXPANSION (NEVER-MEMOIZE CUTIL::MY-STRIP-CARS-EXEC) (MAKE-EVENT (PROG2$ (NEVER-MEMOIZE-FN (QUOTE CUTIL::MY-STRIP-CARS-EXEC)) (QUOTE (VALUE-TRIPLE :INVISIBLE))) :CHECK-EXPANSION (VALUE-TRIPLE :INVISIBLE))) (PROGN! (SET-RAW-MODE T) (DEFUN CUTIL::MY-STRIP-CARS (CUTIL::X) (NREVERSE (CUTIL::MY-STRIP-CARS-EXEC CUTIL::X NIL)))) (DEFTTAG NIL))) (LOCAL (IN-THEORY (ENABLE CUTIL::MY-STRIP-CARS CUTIL::MY-STRIP-CARS-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS-OF-CONS)))))) (RECORD-EXPANSION (MAKE-EVENT (LET* ((XDOC::NAME (QUOTE CUTIL::MY-STRIP-CARS)) (XDOC::PARENTS (QUOTE (UNDOCUMENTED))) (XDOC::SHORT (QUOTE "@(call MY-STRIP-CARS) maps @(see COMMON-LISP::CAR) across a list.")) (XDOC::EXTENSION (QUOTE NIL)) (XDOC::WRLD (W STATE)) (XDOC::TRIPS (REVERSED-WORLD-SINCE-EVENT XDOC::WRLD (QUOTE (TABLE INTRO-TABLE :MARK (QUOTE CUTIL::MY-STRIP-CARS))) NIL)) (XDOC::INFO (REVERSE (NEW-FORMULA-INFO XDOC::TRIPS XDOC::WRLD NIL))) (XDOC::AUTODOC (XDOC::FORMULA-INFO-TO-DEFS (NOT XDOC::EXTENSION) XDOC::INFO)) (XDOC::LONG (CONCATENATE (QUOTE STRING) (QUOTE "<p>This is an ordinary @(see defprojection).</p>") (COERCE (LIST #\Newline #\Newline) (QUOTE STRING)) XDOC::AUTODOC))) (IF XDOC::EXTENSION (CONS (QUOTE XDOC-EXTEND) (CONS XDOC::EXTENSION (CONS XDOC::LONG (QUOTE NIL)))) (CONS (QUOTE DEFXDOC) (CONS XDOC::NAME (CONS (QUOTE :PARENTS) (CONS XDOC::PARENTS (CONS (QUOTE :SHORT) (CONS XDOC::SHORT (CONS (QUOTE :LONG) (CONS XDOC::LONG (QUOTE NIL)))))))))))) (WITH-OUTPUT :OFF (EVENT SUMMARY) (PROGN (TABLE XDOC (QUOTE DOC) (CONS (QUOTE ((:NAME . CUTIL::MY-STRIP-CARS) (:BASE-PKG . CUTIL::ACL2-PKG-WITNESS) (:PARENTS UNDOCUMENTED) (:SHORT . "@(call MY-STRIP-CARS) maps @(see COMMON-LISP::CAR) across a list.") (:LONG . "<p>This is an ordinary @(see defprojection).</p>

<h3>Definitions and Theorems</h3>@(def |CUTIL|::|MY-STRIP-CARS-EXEC|)
@(def |CUTIL|::|MY-STRIP-CARS|)
@(def |CUTIL|::|MY-STRIP-CARS-WHEN-NOT-CONSP|)
@(def |CUTIL|::|MY-STRIP-CARS-OF-CONS|)
@(def |CUTIL|::|TRUE-LISTP-OF-MY-STRIP-CARS|)
@(def |CUTIL|::|LEN-OF-MY-STRIP-CARS|)
@(def |CUTIL|::|CONSP-OF-MY-STRIP-CARS|)
@(def |CUTIL|::|CAR-OF-MY-STRIP-CARS|)
@(def |CUTIL|::|CDR-OF-MY-STRIP-CARS|)
@(def |CUTIL|::|MY-STRIP-CARS-UNDER-IFF|)
@(def |CUTIL|::|MY-STRIP-CARS-OF-LIST-FIX|)
@(def |CUTIL|::|MY-STRIP-CARS-OF-APPEND|)
@(def |CUTIL|::|MY-STRIP-CARS-OF-REV|)
@(def |CUTIL|::|MY-STRIP-CARS-OF-REVAPPEND|)
@(def |CUTIL|::|TAKE-OF-MY-STRIP-CARS|)
@(def |CUTIL|::|NTHCDR-OF-MY-STRIP-CARS|)
@(def |CUTIL|::|MEMBER-EQUAL-OF-CAR-IN-MY-STRIP-CARS-WHEN-MEMBER-EQUAL|)
@(def |CUTIL|::|SUBSETP-EQUAL-OF-MY-STRIP-CARSS-WHEN-SUBSETP-EQUAL|)
@(def |CUTIL|::|NTH-OF-MY-STRIP-CARS|)
@(def |CUTIL|::|MY-STRIP-CARS-EXEC-REMOVAL|)") (:FROM . "[books]/cutil/defprojection-tests.lisp"))) (XDOC::GET-XDOC-TABLE WORLD))) (VALUE-TRIPLE (QUOTE (DEFXDOC CUTIL::MY-STRIP-CARS)))))) (VALUE-TRIPLE (QUOTE CUTIL::MY-STRIP-CARS))))) (27 RECORD-EXPANSION (CUTIL::DEFPROJECTION CUTIL::MY-STRIP-CARS2 (CUTIL::X) (CUTIL::F CUTIL::X) :NIL-PRESERVINGP T :GUARD (ALISTP CUTIL::X)) (WITH-OUTPUT :STACK :PUSH :OFF :ALL :ON ERROR (PROGN (TABLE INTRO-TABLE :MARK (QUOTE CUTIL::MY-STRIP-CARS2)) (RECORD-EXPANSION (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (LOGIC) (DEFUND CUTIL::MY-STRIP-CARS2-EXEC (CUTIL::X CUTIL::ACC) (DECLARE (XARGS :GUARD (ALISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (IF (CONSP CUTIL::X) (CUTIL::MY-STRIP-CARS2-EXEC (CDR CUTIL::X) (CONS (CUTIL::F (CAR CUTIL::X)) CUTIL::ACC)) CUTIL::ACC)) (DEFUND CUTIL::MY-STRIP-CARS2 (CUTIL::X) (DECLARE (XARGS :GUARD (ALISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (MBE :LOGIC (IF (CONSP CUTIL::X) (CONS (CUTIL::F (CAR CUTIL::X)) (CUTIL::MY-STRIP-CARS2 (CDR CUTIL::X))) NIL) :EXEC (REVERSE (CUTIL::MY-STRIP-CARS2-EXEC CUTIL::X NIL)))) (SET-INHIBIT-WARNINGS "disable") (LOCAL (CUTIL::MAYBE-DEFTHM-AS-REWRITE CUTIL::MY-STRIP-CARS2-NIL-PRESERVINGP-LEMMA (EQUAL (CUTIL::F (QUOTE NIL)) NIL))) (LOCAL (MAKE-EVENT (IF (CUTIL::IS-THEOREM-P (QUOTE CUTIL::MY-STRIP-CARS2-NIL-PRESERVINGP-LEMMA) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (DEFTHM CUTIL::MY-STRIP-CARS2-NIL-PRESERVINGP-LEMMA (OR (EQUAL (ALISTP CUTIL::X) T) (EQUAL (ALISTP CUTIL::X) NIL)) :RULE-CLASSES :TYPE-PRESCRIPTION :HINTS (("Goal" :IN-THEORY (QUOTE ((:TYPE-PRESCRIPTION ALISTP))))))))))) (DEFTHM CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP (IMPLIES (NOT (CONSP CUTIL::X)) (EQUAL (CUTIL::MY-STRIP-CARS2 CUTIL::X) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS2)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MY-STRIP-CARS2-OF-CONS (EQUAL (CUTIL::MY-STRIP-CARS2 (CONS CUTIL::A CUTIL::X)) (CONS (CUTIL::F CUTIL::A) (CUTIL::MY-STRIP-CARS2 CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS2)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::TRUE-LISTP-OF-MY-STRIP-CARS2 (EQUAL (TRUE-LISTP (CUTIL::MY-STRIP-CARS2 CUTIL::X)) T) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::LEN-OF-MY-STRIP-CARS2 (EQUAL (LEN (CUTIL::MY-STRIP-CARS2 CUTIL::X)) (LEN CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CONSP-OF-MY-STRIP-CARS2 (EQUAL (CONSP (CUTIL::MY-STRIP-CARS2 CUTIL::X)) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CAR-OF-MY-STRIP-CARS2 (EQUAL (CAR (CUTIL::MY-STRIP-CARS2 CUTIL::X)) (CUTIL::F (CAR CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS2-OF-CONS CUTIL::MY-STRIP-CARS2-NIL-PRESERVINGP-LEMMA DEFAULT-CAR)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CDR-OF-MY-STRIP-CARS2 (EQUAL (CDR (CUTIL::MY-STRIP-CARS2 CUTIL::X)) (CUTIL::MY-STRIP-CARS2 (CDR CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MY-STRIP-CARS2-UNDER-IFF (IFF (CUTIL::MY-STRIP-CARS2 CUTIL::X) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MY-STRIP-CARS2-OF-LIST-FIX (EQUAL (CUTIL::MY-STRIP-CARS2 (LIST-FIX CUTIL::X)) (CUTIL::MY-STRIP-CARS2 CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MY-STRIP-CARS2-OF-APPEND (EQUAL (CUTIL::MY-STRIP-CARS2 (APPEND CUTIL::X CUTIL::Y)) (APPEND (CUTIL::MY-STRIP-CARS2 CUTIL::X) (CUTIL::MY-STRIP-CARS2 CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MY-STRIP-CARS2-OF-REV (EQUAL (CUTIL::MY-STRIP-CARS2 (REV CUTIL::X)) (REV (CUTIL::MY-STRIP-CARS2 CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS2-OF-APPEND CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MY-STRIP-CARS2-OF-REVAPPEND (EQUAL (CUTIL::MY-STRIP-CARS2 (REVAPPEND CUTIL::X CUTIL::Y)) (REVAPPEND (CUTIL::MY-STRIP-CARS2 CUTIL::X) (CUTIL::MY-STRIP-CARS2 CUTIL::Y))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS2-OF-APPEND CUTIL::MY-STRIP-CARS2-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::TAKE-OF-MY-STRIP-CARS2 (EQUAL (TAKE CUTIL::N (CUTIL::MY-STRIP-CARS2 CUTIL::X)) (CUTIL::MY-STRIP-CARS2 (TAKE CUTIL::N CUTIL::X))) :HINTS (("Goal" :INDUCT (TAKE CUTIL::N CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (TAKE-REDEFINITION CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS2-OF-CONS CUTIL::MY-STRIP-CARS2-NIL-PRESERVINGP-LEMMA DEFAULT-CAR)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::NTHCDR-OF-MY-STRIP-CARS2 (EQUAL (NTHCDR CUTIL::N (CUTIL::MY-STRIP-CARS2 CUTIL::X)) (CUTIL::MY-STRIP-CARS2 (NTHCDR CUTIL::N CUTIL::X))) :HINTS (("Goal" :INDUCT (NTHCDR CUTIL::N CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (NTHCDR CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MEMBER-EQUAL-OF-F-IN-MY-STRIP-CARS2-WHEN-MEMBER-EQUAL (IMPLIES (MEMBER-EQUAL CUTIL::A (DOUBLE-REWRITE CUTIL::X)) (MEMBER-EQUAL (CUTIL::F CUTIL::A) (CUTIL::MY-STRIP-CARS2 CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (MEMBER-EQUAL CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SUBSETP-EQUAL-OF-MY-STRIP-CARS2S-WHEN-SUBSETP-EQUAL (IMPLIES (SUBSETP-EQUAL (DOUBLE-REWRITE CUTIL::X) (DOUBLE-REWRITE CUTIL::Y)) (SUBSETP-EQUAL (CUTIL::MY-STRIP-CARS2 CUTIL::X) (CUTIL::MY-STRIP-CARS2 CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (SUBSETP-EQUAL CUTIL::MEMBER-EQUAL-OF-F-IN-MY-STRIP-CARS2-WHEN-MEMBER-EQUAL CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::NTH-OF-MY-STRIP-CARS2 (EQUAL (NTH CUTIL::N (CUTIL::MY-STRIP-CARS2 CUTIL::X)) (CUTIL::F (NTH CUTIL::N CUTIL::X))) :HINTS (("Goal" :INDUCT (NTH CUTIL::N CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (NTH CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS2-OF-CONS CUTIL::MY-STRIP-CARS2-NIL-PRESERVINGP-LEMMA DEFAULT-CAR)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MY-STRIP-CARS2-EXEC-REMOVAL (EQUAL (CUTIL::MY-STRIP-CARS2-EXEC CUTIL::X CUTIL::ACC) (REVAPPEND (CUTIL::MY-STRIP-CARS2 CUTIL::X) CUTIL::ACC)) :HINTS (("Goal" :INDUCT (CUTIL::MY-STRIP-CARS2-EXEC CUTIL::X CUTIL::ACC) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS2-EXEC CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (VERIFY-GUARDS CUTIL::MY-STRIP-CARS2-EXEC :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS2-EXEC)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (VERIFY-GUARDS CUTIL::MY-STRIP-CARS2 :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS2 CUTIL::MY-STRIP-CARS2-EXEC-REMOVAL CUTIL::TRUE-LISTP-OF-MY-STRIP-CARS2 REVERSE-REMOVAL REVAPPEND-REMOVAL REV-OF-APPEND REV-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (PROGN (MAKE-EVENT (IF (GLOBAL-VAL (QUOTE INCLUDE-BOOK-PATH) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::MY-STRIP-CARS2) (QUOTE (DEFUN CUTIL::MY-STRIP-CARS2 (CUTIL::X) (NREVERSE (CUTIL::MY-STRIP-CARS2-EXEC CUTIL::X NIL)))))))))) (DEFTTAG CUTIL::CUTIL-OPTIMIZE) (NEVER-MEMOIZE CUTIL::MY-STRIP-CARS2-EXEC) (PROGN! (SET-RAW-MODE T) (DEFUN CUTIL::MY-STRIP-CARS2 (CUTIL::X) (NREVERSE (CUTIL::MY-STRIP-CARS2-EXEC CUTIL::X NIL)))) (DEFTTAG NIL)) (LOCAL (IN-THEORY (ENABLE CUTIL::MY-STRIP-CARS2 CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS2-OF-CONS))))) (WITH-OUTPUT :STACK :POP (ENCAPSULATE NIL (VALUE-TRIPLE :INVISIBLE) (LOGIC) (DEFUND CUTIL::MY-STRIP-CARS2-EXEC (CUTIL::X CUTIL::ACC) (DECLARE (XARGS :GUARD (ALISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (IF (CONSP CUTIL::X) (CUTIL::MY-STRIP-CARS2-EXEC (CDR CUTIL::X) (CONS (CUTIL::F (CAR CUTIL::X)) CUTIL::ACC)) CUTIL::ACC)) (DEFUND CUTIL::MY-STRIP-CARS2 (CUTIL::X) (DECLARE (XARGS :GUARD (ALISTP CUTIL::X) :MODE :LOGIC :NORMALIZE NIL :VERIFY-GUARDS NIL)) (MBE :LOGIC (IF (CONSP CUTIL::X) (CONS (CUTIL::F (CAR CUTIL::X)) (CUTIL::MY-STRIP-CARS2 (CDR CUTIL::X))) NIL) :EXEC (REVERSE (CUTIL::MY-STRIP-CARS2-EXEC CUTIL::X NIL)))) (SET-INHIBIT-WARNINGS "disable") (RECORD-EXPANSION (LOCAL (CUTIL::MAYBE-DEFTHM-AS-REWRITE CUTIL::MY-STRIP-CARS2-NIL-PRESERVINGP-LEMMA (EQUAL (CUTIL::F (QUOTE NIL)) NIL))) (LOCAL (VALUE-TRIPLE :ELIDED))) (RECORD-EXPANSION (LOCAL (MAKE-EVENT (IF (CUTIL::IS-THEOREM-P (QUOTE CUTIL::MY-STRIP-CARS2-NIL-PRESERVINGP-LEMMA) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (DEFTHM CUTIL::MY-STRIP-CARS2-NIL-PRESERVINGP-LEMMA (OR (EQUAL (ALISTP CUTIL::X) T) (EQUAL (ALISTP CUTIL::X) NIL)) :RULE-CLASSES :TYPE-PRESCRIPTION :HINTS (("Goal" :IN-THEORY (QUOTE ((:TYPE-PRESCRIPTION ALISTP))))))))))) (LOCAL (VALUE-TRIPLE :ELIDED))) (DEFTHM CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP (IMPLIES (NOT (CONSP CUTIL::X)) (EQUAL (CUTIL::MY-STRIP-CARS2 CUTIL::X) NIL)) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS2)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MY-STRIP-CARS2-OF-CONS (EQUAL (CUTIL::MY-STRIP-CARS2 (CONS CUTIL::A CUTIL::X)) (CONS (CUTIL::F CUTIL::A) (CUTIL::MY-STRIP-CARS2 CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS2)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::TRUE-LISTP-OF-MY-STRIP-CARS2 (EQUAL (TRUE-LISTP (CUTIL::MY-STRIP-CARS2 CUTIL::X)) T) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::LEN-OF-MY-STRIP-CARS2 (EQUAL (LEN (CUTIL::MY-STRIP-CARS2 CUTIL::X)) (LEN CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CONSP-OF-MY-STRIP-CARS2 (EQUAL (CONSP (CUTIL::MY-STRIP-CARS2 CUTIL::X)) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CAR-OF-MY-STRIP-CARS2 (EQUAL (CAR (CUTIL::MY-STRIP-CARS2 CUTIL::X)) (CUTIL::F (CAR CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS2-OF-CONS CUTIL::MY-STRIP-CARS2-NIL-PRESERVINGP-LEMMA DEFAULT-CAR)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::CDR-OF-MY-STRIP-CARS2 (EQUAL (CDR (CUTIL::MY-STRIP-CARS2 CUTIL::X)) (CUTIL::MY-STRIP-CARS2 (CDR CUTIL::X))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MY-STRIP-CARS2-UNDER-IFF (IFF (CUTIL::MY-STRIP-CARS2 CUTIL::X) (CONSP CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MY-STRIP-CARS2-OF-LIST-FIX (EQUAL (CUTIL::MY-STRIP-CARS2 (LIST-FIX CUTIL::X)) (CUTIL::MY-STRIP-CARS2 CUTIL::X)) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MY-STRIP-CARS2-OF-APPEND (EQUAL (CUTIL::MY-STRIP-CARS2 (APPEND CUTIL::X CUTIL::Y)) (APPEND (CUTIL::MY-STRIP-CARS2 CUTIL::X) (CUTIL::MY-STRIP-CARS2 CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MY-STRIP-CARS2-OF-REV (EQUAL (CUTIL::MY-STRIP-CARS2 (REV CUTIL::X)) (REV (CUTIL::MY-STRIP-CARS2 CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS2-OF-APPEND CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MY-STRIP-CARS2-OF-REVAPPEND (EQUAL (CUTIL::MY-STRIP-CARS2 (REVAPPEND CUTIL::X CUTIL::Y)) (REVAPPEND (CUTIL::MY-STRIP-CARS2 CUTIL::X) (CUTIL::MY-STRIP-CARS2 CUTIL::Y))) :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS2-OF-APPEND CUTIL::MY-STRIP-CARS2-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::TAKE-OF-MY-STRIP-CARS2 (EQUAL (TAKE CUTIL::N (CUTIL::MY-STRIP-CARS2 CUTIL::X)) (CUTIL::MY-STRIP-CARS2 (TAKE CUTIL::N CUTIL::X))) :HINTS (("Goal" :INDUCT (TAKE CUTIL::N CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (TAKE-REDEFINITION CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS2-OF-CONS CUTIL::MY-STRIP-CARS2-NIL-PRESERVINGP-LEMMA DEFAULT-CAR)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::NTHCDR-OF-MY-STRIP-CARS2 (EQUAL (NTHCDR CUTIL::N (CUTIL::MY-STRIP-CARS2 CUTIL::X)) (CUTIL::MY-STRIP-CARS2 (NTHCDR CUTIL::N CUTIL::X))) :HINTS (("Goal" :INDUCT (NTHCDR CUTIL::N CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (NTHCDR CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MEMBER-EQUAL-OF-F-IN-MY-STRIP-CARS2-WHEN-MEMBER-EQUAL (IMPLIES (MEMBER-EQUAL CUTIL::A (DOUBLE-REWRITE CUTIL::X)) (MEMBER-EQUAL (CUTIL::F CUTIL::A) (CUTIL::MY-STRIP-CARS2 CUTIL::X))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (MEMBER-EQUAL CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::SUBSETP-EQUAL-OF-MY-STRIP-CARS2S-WHEN-SUBSETP-EQUAL (IMPLIES (SUBSETP-EQUAL (DOUBLE-REWRITE CUTIL::X) (DOUBLE-REWRITE CUTIL::Y)) (SUBSETP-EQUAL (CUTIL::MY-STRIP-CARS2 CUTIL::X) (CUTIL::MY-STRIP-CARS2 CUTIL::Y))) :HINTS (("Goal" :INDUCT (LEN CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (SUBSETP-EQUAL CUTIL::MEMBER-EQUAL-OF-F-IN-MY-STRIP-CARS2-WHEN-MEMBER-EQUAL CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::NTH-OF-MY-STRIP-CARS2 (EQUAL (NTH CUTIL::N (CUTIL::MY-STRIP-CARS2 CUTIL::X)) (CUTIL::F (NTH CUTIL::N CUTIL::X))) :HINTS (("Goal" :INDUCT (NTH CUTIL::N CUTIL::X) :IN-THEORY (UNION-THEORIES (QUOTE (NTH CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS2-OF-CONS CUTIL::MY-STRIP-CARS2-NIL-PRESERVINGP-LEMMA DEFAULT-CAR)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (DEFTHM CUTIL::MY-STRIP-CARS2-EXEC-REMOVAL (EQUAL (CUTIL::MY-STRIP-CARS2-EXEC CUTIL::X CUTIL::ACC) (REVAPPEND (CUTIL::MY-STRIP-CARS2 CUTIL::X) CUTIL::ACC)) :HINTS (("Goal" :INDUCT (CUTIL::MY-STRIP-CARS2-EXEC CUTIL::X CUTIL::ACC) :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS2-EXEC CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS2-OF-CONS)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))))) (VERIFY-GUARDS CUTIL::MY-STRIP-CARS2-EXEC :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS2-EXEC)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (VERIFY-GUARDS CUTIL::MY-STRIP-CARS2 :HINTS (("Goal" :IN-THEORY (UNION-THEORIES (QUOTE (CUTIL::MY-STRIP-CARS2 CUTIL::MY-STRIP-CARS2-EXEC-REMOVAL CUTIL::TRUE-LISTP-OF-MY-STRIP-CARS2 REVERSE-REMOVAL REVAPPEND-REMOVAL REV-OF-APPEND REV-OF-REV)) (THEORY (QUOTE CUTIL::DEFPROJECTION-THEORY)))) (AND STABLE-UNDER-SIMPLIFICATIONP (QUOTE (:IN-THEORY (ENABLE)))))) (RECORD-EXPANSION (PROGN (MAKE-EVENT (IF (GLOBAL-VAL (QUOTE INCLUDE-BOOK-PATH) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::MY-STRIP-CARS2) (QUOTE (DEFUN CUTIL::MY-STRIP-CARS2 (CUTIL::X) (NREVERSE (CUTIL::MY-STRIP-CARS2-EXEC CUTIL::X NIL)))))))))) (DEFTTAG CUTIL::CUTIL-OPTIMIZE) (NEVER-MEMOIZE CUTIL::MY-STRIP-CARS2-EXEC) (PROGN! (SET-RAW-MODE T) (DEFUN CUTIL::MY-STRIP-CARS2 (CUTIL::X) (NREVERSE (CUTIL::MY-STRIP-CARS2-EXEC CUTIL::X NIL)))) (DEFTTAG NIL)) (PROGN (RECORD-EXPANSION (MAKE-EVENT (IF (GLOBAL-VAL (QUOTE INCLUDE-BOOK-PATH) (W STATE)) (VALUE (QUOTE (VALUE-TRIPLE :INVISIBLE))) (VALUE (QUOTE (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::MY-STRIP-CARS2) (QUOTE (DEFUN CUTIL::MY-STRIP-CARS2 (CUTIL::X) (NREVERSE (CUTIL::MY-STRIP-CARS2-EXEC CUTIL::X NIL)))))))))) (VALUE-TRIPLE (CW "~|~%Optimizing definition of ~s0:~%  ~p1~%~%" (QUOTE CUTIL::MY-STRIP-CARS2) (QUOTE (DEFUN CUTIL::MY-STRIP-CARS2 (CUTIL::X) (NREVERSE (CUTIL::MY-STRIP-CARS2-EXEC CUTIL::X NIL))))))) (DEFTTAG CUTIL::CUTIL-OPTIMIZE) (RECORD-EXPANSION (NEVER-MEMOIZE CUTIL::MY-STRIP-CARS2-EXEC) (MAKE-EVENT (PROG2$ (NEVER-MEMOIZE-FN (QUOTE CUTIL::MY-STRIP-CARS2-EXEC)) (QUOTE (VALUE-TRIPLE :INVISIBLE))) :CHECK-EXPANSION (VALUE-TRIPLE :INVISIBLE))) (PROGN! (SET-RAW-MODE T) (DEFUN CUTIL::MY-STRIP-CARS2 (CUTIL::X) (NREVERSE (CUTIL::MY-STRIP-CARS2-EXEC CUTIL::X NIL)))) (DEFTTAG NIL))) (LOCAL (IN-THEORY (ENABLE CUTIL::MY-STRIP-CARS2 CUTIL::MY-STRIP-CARS2-WHEN-NOT-CONSP CUTIL::MY-STRIP-CARS2-OF-CONS)))))) (RECORD-EXPANSION (MAKE-EVENT (LET* ((XDOC::NAME (QUOTE CUTIL::MY-STRIP-CARS2)) (XDOC::PARENTS (QUOTE (UNDOCUMENTED))) (XDOC::SHORT (QUOTE "@(call MY-STRIP-CARS2) maps @(see CUTIL::F) across a list.")) (XDOC::EXTENSION (QUOTE NIL)) (XDOC::WRLD (W STATE)) (XDOC::TRIPS (REVERSED-WORLD-SINCE-EVENT XDOC::WRLD (QUOTE (TABLE INTRO-TABLE :MARK (QUOTE CUTIL::MY-STRIP-CARS2))) NIL)) (XDOC::INFO (REVERSE (NEW-FORMULA-INFO XDOC::TRIPS XDOC::WRLD NIL))) (XDOC::AUTODOC (XDOC::FORMULA-INFO-TO-DEFS (NOT XDOC::EXTENSION) XDOC::INFO)) (XDOC::LONG (CONCATENATE (QUOTE STRING) (QUOTE "<p>This is an ordinary @(see defprojection).</p>") (COERCE (LIST #\Newline #\Newline) (QUOTE STRING)) XDOC::AUTODOC))) (IF XDOC::EXTENSION (CONS (QUOTE XDOC-EXTEND) (CONS XDOC::EXTENSION (CONS XDOC::LONG (QUOTE NIL)))) (CONS (QUOTE DEFXDOC) (CONS XDOC::NAME (CONS (QUOTE :PARENTS) (CONS XDOC::PARENTS (CONS (QUOTE :SHORT) (CONS XDOC::SHORT (CONS (QUOTE :LONG) (CONS XDOC::LONG (QUOTE NIL)))))))))))) (WITH-OUTPUT :OFF (EVENT SUMMARY) (PROGN (TABLE XDOC (QUOTE DOC) (CONS (QUOTE ((:NAME . CUTIL::MY-STRIP-CARS2) (:BASE-PKG . CUTIL::ACL2-PKG-WITNESS) (:PARENTS UNDOCUMENTED) (:SHORT . "@(call MY-STRIP-CARS2) maps @(see CUTIL::F) across a list.") (:LONG . "<p>This is an ordinary @(see defprojection).</p>

<h3>Definitions and Theorems</h3>@(def |CUTIL|::|MY-STRIP-CARS2-EXEC|)
@(def |CUTIL|::|MY-STRIP-CARS2|)
@(def |CUTIL|::|MY-STRIP-CARS2-WHEN-NOT-CONSP|)
@(def |CUTIL|::|MY-STRIP-CARS2-OF-CONS|)
@(def |CUTIL|::|TRUE-LISTP-OF-MY-STRIP-CARS2|)
@(def |CUTIL|::|LEN-OF-MY-STRIP-CARS2|)
@(def |CUTIL|::|CONSP-OF-MY-STRIP-CARS2|)
@(def |CUTIL|::|CAR-OF-MY-STRIP-CARS2|)
@(def |CUTIL|::|CDR-OF-MY-STRIP-CARS2|)
@(def |CUTIL|::|MY-STRIP-CARS2-UNDER-IFF|)
@(def |CUTIL|::|MY-STRIP-CARS2-OF-LIST-FIX|)
@(def |CUTIL|::|MY-STRIP-CARS2-OF-APPEND|)
@(def |CUTIL|::|MY-STRIP-CARS2-OF-REV|)
@(def |CUTIL|::|MY-STRIP-CARS2-OF-REVAPPEND|)
@(def |CUTIL|::|TAKE-OF-MY-STRIP-CARS2|)
@(def |CUTIL|::|NTHCDR-OF-MY-STRIP-CARS2|)
@(def |CUTIL|::|MEMBER-EQUAL-OF-F-IN-MY-STRIP-CARS2-WHEN-MEMBER-EQUAL|)
@(def |CUTIL|::|SUBSETP-EQUAL-OF-MY-STRIP-CARS2S-WHEN-SUBSETP-EQUAL|)
@(def |CUTIL|::|NTH-OF-MY-STRIP-CARS2|)
@(def |CUTIL|::|MY-STRIP-CARS2-EXEC-REMOVAL|)") (:FROM . "[books]/cutil/defprojection-tests.lisp"))) (XDOC::GET-XDOC-TABLE WORLD))) (VALUE-TRIPLE (QUOTE (DEFXDOC CUTIL::MY-STRIP-CARS2)))))) (VALUE-TRIPLE (QUOTE CUTIL::MY-STRIP-CARS2))))))
(("/usr/share/acl2-6.3/books/cutil/portcullis.lisp" "portcullis" "portcullis" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 1188104018) ("/usr/share/acl2-6.3/books/std/osets/portcullis.lisp" "std/osets/portcullis" "portcullis" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 1689687557) ("/usr/share/acl2-6.3/books/xdoc/portcullis.lisp" "xdoc/portcullis" "portcullis" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 1473208573) ("/usr/share/acl2-6.3/books/str/portcullis.lisp" "str/portcullis" "portcullis" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 2077071243))
(("/usr/share/acl2-6.3/books/cutil/defprojection-tests.lisp" "defprojection-tests" "defprojection-tests" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS (:CUTIL-OPTIMIZE "/usr/share/acl2-6.3/books/cutil/defprojection-tests.lisp"))) . 473381139) ("/usr/share/acl2-6.3/books/cutil/defprojection.lisp" "defprojection" "defprojection" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 854966444) ("/usr/share/acl2-6.3/books/cutil/deflist.lisp" "deflist" "deflist" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 857676809) (LOCAL ("/usr/share/acl2-6.3/books/std/osets/under-set-equiv.lisp" "std/osets/under-set-equiv" "under-set-equiv" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 1595680367)) ("/usr/share/acl2-6.3/books/cutil/maybe-defthm.lisp" "maybe-defthm" "maybe-defthm" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 169275099) ("/usr/share/acl2-6.3/books/misc/assert.lisp" "misc/assert" "assert" ((:SKIPPED-PROOFSP) (:AXIOMSP) (:TTAGS)) . 1184956729) ("/usr/share/acl2-6.3/books/misc/eval.lisp" "eval" "eval" 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