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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, %
% merchantability 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: window infernce rules preserving equality %
%============================================================================%
%$Id: eq_close.ml,v 3.1 1993/12/07 14:15:19 jg Exp $%
begin_section eq_close;;
let CONJ1_THM =
prove
(
"!A B C. (B ==> (C = A)) ==> ((C /\ B) = (A /\ B))"
,
(REPEAT GEN_TAC) THEN
BOOL_CASES_TAC "A:bool" THEN
BOOL_CASES_TAC "B:bool" THEN
REWRITE_TAC []
);;
% (B |- C = A) %
% -------------------------- CONJ1_CLOSE "A /\ B" %
% (|- (C /\ B) = (A /\ B)) %
let CONJ1_CLOSE tm th =
let (a,b) = dest_conj tm in
let c = rand (rator (concl th)) in
MP (SPECL [a; b; c] CONJ1_THM) (DISCH b th) ;;
let CONJ2_THM =
prove
(
"!A B C. (A ==> (C = B)) ==> ((A /\ C) = (A /\ B))"
,
(REPEAT GEN_TAC) THEN
BOOL_CASES_TAC "A:bool" THEN
BOOL_CASES_TAC "B:bool" THEN
REWRITE_TAC []
);;
% (A |- C = B) %
% -------------------------- CONJ2_CLOSE "A /\ B" %
% (|- (A /\ C) = (A /\ B)) %
let CONJ2_CLOSE tm th =
let (a,b) = dest_conj tm in
let c = rand (rator (concl th)) in
MP (SPECL [a; b; c] CONJ2_THM) (DISCH a th) ;;
let IMP1_THM =
prove
(
"!A B C. (~B ==> (C = A)) ==> ((C ==> B) = (A ==> B))"
,
(REPEAT GEN_TAC) THEN
BOOL_CASES_TAC "A:bool" THEN
BOOL_CASES_TAC "B:bool" THEN
REWRITE_TAC []
) ;;
% (~B |- C = A) %
% ---------------------------- IMP1_CLOSE "A ==> B" %
% (|- (C ==> B) = (A ==> B)) %
let IMP1_CLOSE tm th =
let (a,b) = dest_imp tm in
let c = (rand (rator (concl th))) in
MP (SPECL [a; b; c] IMP1_THM) (DISCH (mk_neg b) th) ;;
let IMP2_THM =
prove
(
"!A B C. (A ==> (C = B)) ==> ((A ==> C) = (A ==> B))"
,
(REPEAT GEN_TAC) THEN
BOOL_CASES_TAC "A:bool" THEN
BOOL_CASES_TAC "B:bool" THEN
REWRITE_TAC []
) ;;
% (A |- C = B) %
% ---------------------------- IMP2_CLOSE "A ==> B" %
% (|- (A ==> C) = (A ==> B)) %
let IMP2_CLOSE tm th =
let (a,b) = dest_imp tm in
let c = (rand (rator (concl th))) in
MP (SPECL [a; b; c] IMP2_THM) (DISCH a th) ;;
let PMI1_THM =
prove
(
"!A B C. (B ==> (C = A)) ==> ((C <== B) = (A <== B))"
,
(REPEAT GEN_TAC) THEN
(PURE_REWRITE_TAC [PMI_DEF]) THEN
BOOL_CASES_TAC "A:bool" THEN
BOOL_CASES_TAC "B:bool" THEN
REWRITE_TAC []
) ;;
% (B |- C = A) %
% ---------------------------- PMI1_CLOSE "A <== B" %
% (|- (C <== B) = (A <== B)) %
let PMI1_CLOSE tm th =
let (a,b) = dest_pmi tm in
let c = (rand (rator (concl th))) in
MP (SPECL [a; b; c] PMI1_THM) (DISCH b th) ;;
let PMI2_THM =
prove
(
"!A B C. (~A ==> (C = B)) ==> ((A <== C) = (A <== B))"
,
(REPEAT GEN_TAC) THEN
(PURE_REWRITE_TAC [PMI_DEF]) THEN
BOOL_CASES_TAC "A:bool" THEN
BOOL_CASES_TAC "B:bool" THEN
REWRITE_TAC []
) ;;
% (~A |- C = B) %
% ---------------------------- PMI2_CLOSE "A <== B" %
% (|- (A <== C) = (A <== B)) %
let PMI2_CLOSE tm th =
let (a,b) = dest_pmi tm in
let c = (rand (rator (concl th))) in
MP (SPECL [a; b; c] PMI2_THM) (DISCH (mk_neg a) th) ;;
let DISJ1_THM =
prove
(
"!A B C. (~B ==> (C = A)) ==> ((C \/ B) = (A \/ B))"
,
(REPEAT GEN_TAC) THEN
BOOL_CASES_TAC "A:bool" THEN
BOOL_CASES_TAC "B:bool" THEN
REWRITE_TAC []
) ;;
% (~B |- C = A) %
% -------------------------- DISJ1_CLOSE "A \/ B" %
% (|- (C \/ B) = (A \/ B)) %
let DISJ1_CLOSE tm th =
let (a,b) = dest_disj tm in
let c = (rand (rator (concl th))) in
MP (SPECL [a; b; c] DISJ1_THM) (DISCH (mk_neg b) th) ;;
let DISJ2_THM =
prove
(
"!A B C. (~A ==> (C = B)) ==> ((A \/ C) = (A \/ B))"
,
(REPEAT GEN_TAC) THEN
BOOL_CASES_TAC "A:bool" THEN
BOOL_CASES_TAC "B:bool" THEN
REWRITE_TAC []
) ;;
% (~A |- C = B) %
% --------------------------- DISJ2_CLOSE "A \/ B" %
% (|- (A \/ C) = (A \/ B)) %
let DISJ2_CLOSE tm th =
let (a,b) = dest_disj tm in
let c = (rand (rator (concl th))) in
MP (SPECL [a; b; c] DISJ2_THM) (DISCH (mk_neg a) th) ;;
% Put all those rules in the data base. %
store_rule
(
[RATOR; RAND],
is_conj,
K (K equiv_tm),
K (K equiv_tm),
(\tm.\tl. (SMASH (ASSUME (rand tm))) @ tl),
K [],
CONJ1_CLOSE
);;
store_rule
(
[RAND],
is_conj,
K (K equiv_tm),
K (K equiv_tm),
(\tm.\tl. (SMASH (ASSUME (rand (rator tm)))) @ tl),
K [],
CONJ2_CLOSE
);;
store_rule
(
[RATOR; RAND],
is_trueimp,
K (K equiv_tm),
K (K equiv_tm),
(\tm.\tl. (SMASH (ASSUME (mk_neg (rand tm)))) @ tl),
K [],
IMP1_CLOSE
);;
store_rule
(
[RAND],
is_trueimp,
K (K equiv_tm),
K (K equiv_tm),
(\tm.\tl. (SMASH (ASSUME (rand (rator tm)))) @ tl),
K [],
IMP2_CLOSE
);;
store_rule
(
[RATOR; RAND],
is_pmi,
K (K equiv_tm),
K (K equiv_tm),
(\tm.\tl. (SMASH (ASSUME (rand tm))) @ tl),
K [],
PMI1_CLOSE
);;
store_rule
(
[RAND],
is_pmi,
K (K equiv_tm),
K (K equiv_tm),
(\tm.\tl. (SMASH (ASSUME (mk_neg (rand (rator tm))))) @ tl),
K [],
PMI2_CLOSE
);;
store_rule
(
[RATOR; RAND],
is_disj,
K (K equiv_tm),
K (K equiv_tm),
(\tm.\tl. (SMASH (ASSUME (mk_neg (rand tm)))) @ tl),
K [],
DISJ1_CLOSE
);;
store_rule
(
[RAND],
is_disj,
K (K equiv_tm),
K (K equiv_tm),
(\tm.\tl. (SMASH (ASSUME (mk_neg (rand (rator tm))))) @ tl),
K [],
DISJ2_CLOSE
);;
end_section eq_close.ml
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