/usr/share/hol88-2.02.19940316/Library/pair/both1.ml is in hol88-library-source 2.02.19940316-19.
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% Copyright (c) Jim Grundy 1992 %
% All rights reserved %
% %
% Jim Grundy, hereafter referred to as `the Author', retains the %
% copyright and all other legal rights to the Software contained in %
% this file, hereafter referred to as `the Software'. %
% %
% The Software is made available free of charge on an `as is' basis. %
% No guarantee, either express or implied, of maintenance, reliability %
% or suitability for any purpose is made by the Author. %
% %
% The user is granted the right to make personal or internal use %
% of the Software provided that both: %
% 1. The Software is not used for commercial gain. %
% 2. The user shall not hold the Author liable for any consequences %
% arising from use of the Software. %
% %
% The user is granted the right to further distribute the Software %
% provided that both: %
% 1. The Software and this statement of rights is not modified. %
% 2. The Software does not form part or the whole of a system %
% distributed for commercial gain. %
% %
% The user is granted the right to modify the Software for personal or %
% internal use provided that all of the following conditions are %
% observed: %
% 1. The user does not distribute the modified software. %
% 2. The modified software is not used for commercial gain. %
% 3. The Author retains all rights to the modified software. %
% %
% Anyone seeking a licence to use this software for commercial purposes %
% is invited to contact the Author. %
% --------------------------------------------------------------------- %
% CONTENTS: functions which are common to paried universal and %
% existentail quantifications. %
% --------------------------------------------------------------------- %
%$Id: both1.ml,v 3.1 1993/12/07 14:42:10 jg Exp $%
% ------------------------------------------------------------------------- %
% PFORALL_THM = |- !f. (!x y. f x y) = (!(x,y). f x y) %
% ------------------------------------------------------------------------- %
let PFORALL_THM =
prove
(
"!f. (!(x:*) (y:**). f x y) = (!(x:*,y:**). f x y)"
,
GEN_TAC THEN
EQ_TAC THENL
[
DISCH_TAC THEN
(REWRITE_TAC [FORALL_DEF]) THEN
BETA_TAC THEN
(ASM_REWRITE_TAC []) THEN
(CONV_TAC (RAND_CONV (PALPHA_CONV "(x:*,y:**)"))) THEN
REFL_TAC
;
(CONV_TAC (RATOR_CONV (RAND_CONV (GEN_PALPHA_CONV "z:*#**")))) THEN
DISCH_TAC THEN
(CONV_TAC (RAND_CONV (ABS_CONV (RAND_CONV (ABS_CONV
(RATOR_CONV (RAND_CONV (\tm. (SYM (SPEC_ALL FST)))))))))) THEN
(CONV_TAC (RAND_CONV (ABS_CONV (RAND_CONV (ABS_CONV
(RAND_CONV (\tm. (SYM (SPEC_ALL SND))))))))) THEN
(ASM_REWRITE_TAC [])
]
);;
% ------------------------------------------------------------------------- %
% PEXISTS_THM = |- !f. (?x y. f x y) = (?(x,y). f x y) %
% ------------------------------------------------------------------------- %
let PEXISTS_THM =
prove
(
"!f. (?(x:*) (y:**). f x y) = (?(x:*,y:**). f x y)"
,
GEN_TAC THEN
EQ_TAC THENL
[
(CONV_TAC LEFT_IMP_EXISTS_CONV) THEN
GEN_TAC THEN
(CONV_TAC LEFT_IMP_EXISTS_CONV) THEN
GEN_TAC THEN
DISCH_TAC THEN
(CONV_TAC (GEN_PALPHA_CONV "a:*#**")) THEN
(EXISTS_TAC "(x:*,y:**)") THEN
(ASM_REWRITE_TAC [FST; SND])
;
(CONV_TAC (RATOR_CONV (RAND_CONV (GEN_PALPHA_CONV "a:*#**")))) THEN
(CONV_TAC LEFT_IMP_EXISTS_CONV) THEN
GEN_TAC THEN
DISCH_TAC THEN
(EXISTS_TAC "FST (a:*#**)") THEN
(EXISTS_TAC "SND (a:*#**)") THEN
(ASM_REWRITE_TAC [])
]
);;
% ------------------------------------------------------------------------- %
% CURRY_FORALL_CONV "!(x,y).t" = (|- (!(x,y).t) = (!x y.t)) %
% ------------------------------------------------------------------------- %
let CURRY_FORALL_CONV tm =
(let (xy,bod) = dest_pforall tm in
let (x,y) = dest_pair xy in
let result = list_mk_pforall ([x;y],bod) in
let f = rand (rand tm) in
let th1 = RAND_CONV (PABS_CONV (UNPBETA_CONV xy)) tm in
let th2 = CONV_RULE (RAND_CONV (RAND_CONV (PABS_CONV CURRY_CONV))) th1 in
let th3 = (SYM (ISPEC f PFORALL_THM)) in
let th4 = CONV_RULE (RATOR_CONV (RAND_CONV (GEN_PALPHA_CONV xy))) th3 in
let th5 = CONV_RULE (RAND_CONV (GEN_PALPHA_CONV x)) (th2 TRANS th4) in
let th6 = CONV_RULE (RAND_CONV (RAND_CONV (PABS_CONV
(GEN_PALPHA_CONV y)))) th5 in
let th7 = CONV_RULE (RAND_CONV (RAND_CONV (PABS_CONV (RAND_CONV (PABS_CONV
(RATOR_CONV PBETA_CONV)))))) th6 in
let th8 =
CONV_RULE (RAND_CONV (RAND_CONV (PABS_CONV (RAND_CONV (PABS_CONV
PBETA_CONV))))) th7
in
th8 TRANS (REFL result)
)? failwith `CURRY_FORALL_CONV` ;;
% ------------------------------------------------------------------------- %
% CURRY_EXISTS_CONV "?(x,y).t" = (|- (?(x,y).t) = (?x y.t)) %
% ------------------------------------------------------------------------- %
let CURRY_EXISTS_CONV tm =
(let (xy,bod) = dest_pexists tm in
let (x,y) = dest_pair xy in
let result = list_mk_pexists ([x;y],bod) in
let f = rand (rand tm) in
let th1 = RAND_CONV (PABS_CONV (UNPBETA_CONV xy)) tm in
let th2 = CONV_RULE (RAND_CONV (RAND_CONV (PABS_CONV CURRY_CONV))) th1 in
let th3 = (SYM (ISPEC f PEXISTS_THM)) in
let th4 = CONV_RULE (RATOR_CONV (RAND_CONV (GEN_PALPHA_CONV xy))) th3 in
let th5 = CONV_RULE (RAND_CONV (GEN_PALPHA_CONV x)) (th2 TRANS th4) in
let th6 = CONV_RULE (RAND_CONV (RAND_CONV (PABS_CONV
(GEN_PALPHA_CONV y)))) th5 in
let th7 = CONV_RULE (RAND_CONV (RAND_CONV (PABS_CONV (RAND_CONV (PABS_CONV
(RATOR_CONV PBETA_CONV)))))) th6 in
let th8 = CONV_RULE (RAND_CONV (RAND_CONV (PABS_CONV (RAND_CONV (PABS_CONV
PBETA_CONV))))) th7
in
th8 TRANS (REFL result)
)? failwith `CURRY_EXISTS_CONV` ;;
% ------------------------------------------------------------------------- %
% UNCURRY_FORALL_CONV "!x y.t" = (|- (!x y.t) = (!(x,y).t)) %
% ------------------------------------------------------------------------- %
let UNCURRY_FORALL_CONV tm =
(let (x,(y,bod)) = (I # dest_pforall) (dest_pforall tm) in
let xy = mk_pair(x,y) in
let result = mk_pforall (xy,bod) in
let th1 = (RAND_CONV (PABS_CONV (RAND_CONV (PABS_CONV
(UNPBETA_CONV xy))))) tm in
let f = rand (rator (pbody (rand (pbody (rand (rand (concl th1))))))) in
let th2 = CONV_RULE (RAND_CONV (RAND_CONV (PABS_CONV (RAND_CONV (PABS_CONV
CURRY_CONV))))) th1 in
let th3 = ISPEC f PFORALL_THM in
let th4 = CONV_RULE (RATOR_CONV (RAND_CONV (GEN_PALPHA_CONV x))) th3 in
let th5 = CONV_RULE (RATOR_CONV (RAND_CONV (RAND_CONV (PABS_CONV
(GEN_PALPHA_CONV y))))) th4 in
let th6 = CONV_RULE (RAND_CONV (GEN_PALPHA_CONV xy)) (th2 TRANS th5) in
let th7 = CONV_RULE (RAND_CONV (RAND_CONV (PABS_CONV (RATOR_CONV
PBETA_CONV)))) th6 in
let th8 = CONV_RULE (RAND_CONV (RAND_CONV (PABS_CONV PBETA_CONV))) th7
in
th8 TRANS (REFL result)
) ? failwith `UNCURRY_FORALL_CONV`;;
% ------------------------------------------------------------------------- %
% UNCURRY_EXISTS_CONV "?x y.t" = (|- (?x y.t) = (?(x,y).t)) %
% ------------------------------------------------------------------------- %
let UNCURRY_EXISTS_CONV tm =
(let (x,(y,bod)) = (I # dest_pexists) (dest_pexists tm) in
let xy = mk_pair(x,y) in
let result = mk_pexists (xy,bod) in
let th1 = (RAND_CONV (PABS_CONV (RAND_CONV (PABS_CONV
(UNPBETA_CONV xy))))) tm in
let f = rand (rator (pbody (rand (pbody (rand (rand (concl th1))))))) in
let th2 = CONV_RULE (RAND_CONV (RAND_CONV (PABS_CONV (RAND_CONV (PABS_CONV
CURRY_CONV))))) th1 in
let th3 = ISPEC f PEXISTS_THM in
let th4 = CONV_RULE (RATOR_CONV (RAND_CONV (GEN_PALPHA_CONV x))) th3 in
let th5 = CONV_RULE (RATOR_CONV (RAND_CONV (RAND_CONV (PABS_CONV
(GEN_PALPHA_CONV y))))) th4 in
let th6 = CONV_RULE (RAND_CONV (GEN_PALPHA_CONV xy)) (th2 TRANS th5) in
let th7 = CONV_RULE (RAND_CONV (RAND_CONV (PABS_CONV (RATOR_CONV
PBETA_CONV)))) th6 in
let th8 = CONV_RULE (RAND_CONV (RAND_CONV (PABS_CONV PBETA_CONV))) th7
in
th8 TRANS (REFL result)
) ? failwith `UNCURRY_EXISTS_CONV`;;
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