# HG changeset patch # User paulson # Date 962881892 -7200 # Node ID 53e09e592278ef4cabaafb2b54f8d6dc0f422965 # Parent 8baf94ddb34532de8f728cf80e54a61d4fd8cd47 removal of batch style, and tidying diff -r 8baf94ddb345 -r 53e09e592278 src/FOLP/FOLP.ML --- a/src/FOLP/FOLP.ML Thu Jul 06 12:27:37 2000 +0200 +++ b/src/FOLP/FOLP.ML Thu Jul 06 13:11:32 2000 +0200 @@ -6,48 +6,30 @@ Tactics and lemmas for FOLP (Classical First-Order Logic with Proofs) *) -open FOLP; - -signature FOLP_LEMMAS = - sig - val disjCI : thm - val excluded_middle : thm - val exCI : thm - val ex_classical : thm - val iffCE : thm - val impCE : thm - val notnotD : thm - val swap : thm - end; - - -structure FOLP_Lemmas : FOLP_LEMMAS = -struct - (*** Classical introduction rules for | and EX ***) -val disjCI = prove_goal FOLP.thy - "(!!x. x:~Q ==> f(x):P) ==> ?p : P|Q" - (fn prems=> - [ (rtac classical 1), - (REPEAT (ares_tac (prems@[disjI1,notI]) 1)), - (REPEAT (ares_tac (prems@[disjI2,notE]) 1)) ]); +val prems= goal FOLP.thy + "(!!x. x:~Q ==> f(x):P) ==> ?p : P|Q"; +by (rtac classical 1); +by (REPEAT (ares_tac (prems@[disjI1,notI]) 1)); +by (REPEAT (ares_tac (prems@[disjI2,notE]) 1)) ; +qed "disjCI"; (*introduction rule involving only EX*) -val ex_classical = prove_goal FOLP.thy - "( !!u. u:~(EX x. P(x)) ==> f(u):P(a)) ==> ?p : EX x. P(x)" - (fn prems=> - [ (rtac classical 1), - (eresolve_tac (prems RL [exI]) 1) ]); +val prems= goal FOLP.thy + "( !!u. u:~(EX x. P(x)) ==> f(u):P(a)) ==> ?p : EX x. P(x)"; +by (rtac classical 1); +by (eresolve_tac (prems RL [exI]) 1) ; +qed "ex_classical"; (*version of above, simplifying ~EX to ALL~ *) -val exCI = prove_goal FOLP.thy - "(!!u. u:ALL x. ~P(x) ==> f(u):P(a)) ==> ?p : EX x. P(x)" - (fn [prem]=> - [ (rtac ex_classical 1), - (resolve_tac [notI RS allI RS prem] 1), - (etac notE 1), - (etac exI 1) ]); +val [prem]= goal FOLP.thy + "(!!u. u:ALL x. ~P(x) ==> f(u):P(a)) ==> ?p : EX x. P(x)"; +by (rtac ex_classical 1); +by (resolve_tac [notI RS allI RS prem] 1); +by (etac notE 1); +by (etac exI 1) ; +qed "exCI"; val excluded_middle = prove_goal FOLP.thy "?p : ~P | P" (fn _=> [ rtac disjCI 1, assume_tac 1 ]); @@ -57,39 +39,38 @@ (*Classical implies (-->) elimination. *) -val impCE = prove_goal FOLP.thy - "[| p:P-->Q; !!x. x:~P ==> f(x):R; !!y. y:Q ==> g(y):R |] ==> ?p : R" - (fn major::prems=> - [ (resolve_tac [excluded_middle RS disjE] 1), - (DEPTH_SOLVE (ares_tac (prems@[major RS mp]) 1)) ]); +val major::prems= goal FOLP.thy + "[| p:P-->Q; !!x. x:~P ==> f(x):R; !!y. y:Q ==> g(y):R |] ==> ?p : R"; +by (resolve_tac [excluded_middle RS disjE] 1); +by (DEPTH_SOLVE (ares_tac (prems@[major RS mp]) 1)) ; +qed "impCE"; (*Double negation law*) -val notnotD = prove_goal FOLP.thy "p:~~P ==> ?p : P" - (fn [major]=> - [ (rtac classical 1), (eresolve_tac [major RS notE] 1) ]); +Goal "p:~~P ==> ?p : P"; +by (rtac classical 1); +by (etac notE 1); +by (assume_tac 1); +qed "notnotD"; (*** Tactics for implication and contradiction ***) (*Classical <-> elimination. Proof substitutes P=Q in ~P ==> ~Q and P ==> Q *) -val iffCE = prove_goalw FOLP.thy [iff_def] +val prems = goalw FOLP.thy [iff_def] "[| p:P<->Q; !!x y.[| x:P; y:Q |] ==> f(x,y):R; \ -\ !!x y.[| x:~P; y:~Q |] ==> g(x,y):R |] ==> ?p : R" - (fn prems => - [ (rtac conjE 1), - (REPEAT (DEPTH_SOLVE_1 - (etac impCE 1 ORELSE mp_tac 1 ORELSE ares_tac prems 1))) ]); +\ !!x y.[| x:~P; y:~Q |] ==> g(x,y):R |] ==> ?p : R"; +by (rtac conjE 1); +by (REPEAT (DEPTH_SOLVE_1 (etac impCE 1 + ORELSE mp_tac 1 ORELSE ares_tac prems 1))) ; +qed "iffCE"; (*Should be used as swap since ~P becomes redundant*) -val swap = prove_goal FOLP.thy - "p:~P ==> (!!x. x:~Q ==> f(x):P) ==> ?p : Q" - (fn major::prems=> - [ (rtac classical 1), - (rtac (major RS notE) 1), - (REPEAT (ares_tac prems 1)) ]); +val major::prems= goal FOLP.thy + "p:~P ==> (!!x. x:~Q ==> f(x):P) ==> ?p : Q"; +by (rtac classical 1); +by (rtac (major RS notE) 1); +by (REPEAT (ares_tac prems 1)) ; +qed "swap"; -end; - -open FOLP_Lemmas; diff -r 8baf94ddb345 -r 53e09e592278 src/FOLP/IFOLP.ML --- a/src/FOLP/IFOLP.ML Thu Jul 06 12:27:37 2000 +0200 +++ b/src/FOLP/IFOLP.ML Thu Jul 06 13:11:32 2000 +0200 @@ -5,95 +5,30 @@ Tactics and lemmas for IFOLP (Intuitionistic First-Order Logic with Proofs) *) - -open IFOLP; - -signature IFOLP_LEMMAS = - sig - val allE: thm - val all_cong: thm - val all_dupE: thm - val all_impE: thm - val box_equals: thm - val conjE: thm - val conj_cong: thm - val conj_impE: thm - val contrapos: thm - val disj_cong: thm - val disj_impE: thm - val eq_cong: thm - val ex1I: thm - val ex1E: thm - val ex1_equalsE: thm -(* val ex1_cong: thm****) - val ex_cong: thm - val ex_impE: thm - val iffD1: thm - val iffD2: thm - val iffE: thm - val iffI: thm - val iff_cong: thm - val iff_impE: thm - val iff_refl: thm - val iff_sym: thm - val iff_trans: thm - val impE: thm - val imp_cong: thm - val imp_impE: thm - val mp_tac: int -> tactic - val notE: thm - val notI: thm - val not_cong: thm - val not_impE: thm - val not_sym: thm - val not_to_imp: thm - val pred1_cong: thm - val pred2_cong: thm - val pred3_cong: thm - val pred_congs: thm list - val refl: thm - val rev_mp: thm - val simp_equals: thm - val subst: thm - val ssubst: thm - val subst_context: thm - val subst_context2: thm - val subst_context3: thm - val sym: thm - val trans: thm - val TrueI: thm - val uniq_assume_tac: int -> tactic - val uniq_mp_tac: int -> tactic - end; - - -structure IFOLP_Lemmas : IFOLP_LEMMAS = -struct - -val TrueI = TrueI; - (*** Sequent-style elimination rules for & --> and ALL ***) -val conjE = prove_goal IFOLP.thy - "[| p:P&Q; !!x y.[| x:P; y:Q |] ==> f(x,y):R |] ==> ?a:R" - (fn prems=> - [ (REPEAT (resolve_tac prems 1 - ORELSE (resolve_tac [conjunct1, conjunct2] 1 THEN - resolve_tac prems 1))) ]); +val prems= Goal + "[| p:P&Q; !!x y.[| x:P; y:Q |] ==> f(x,y):R |] ==> ?a:R"; +by (REPEAT (resolve_tac prems 1 + ORELSE (resolve_tac [conjunct1, conjunct2] 1 THEN resolve_tac prems 1))) ; +qed "conjE"; -val impE = prove_goal IFOLP.thy - "[| p:P-->Q; q:P; !!x. x:Q ==> r(x):R |] ==> ?p:R" - (fn prems=> [ (REPEAT (resolve_tac (prems@[mp]) 1)) ]); +val prems= Goal + "[| p:P-->Q; q:P; !!x. x:Q ==> r(x):R |] ==> ?p:R"; +by (REPEAT (resolve_tac (prems@[mp]) 1)) ; +qed "impE"; -val allE = prove_goal IFOLP.thy - "[| p:ALL x. P(x); !!y. y:P(x) ==> q(y):R |] ==> ?p:R" - (fn prems=> [ (REPEAT (resolve_tac (prems@[spec]) 1)) ]); +val prems= Goal + "[| p:ALL x. P(x); !!y. y:P(x) ==> q(y):R |] ==> ?p:R"; +by (REPEAT (resolve_tac (prems@[spec]) 1)) ; +qed "allE"; (*Duplicates the quantifier; for use with eresolve_tac*) -val all_dupE = prove_goal IFOLP.thy +val prems= Goal "[| p:ALL x. P(x); !!y z.[| y:P(x); z:ALL x. P(x) |] ==> q(y,z):R \ -\ |] ==> ?p:R" - (fn prems=> [ (REPEAT (resolve_tac (prems@[spec]) 1)) ]); +\ |] ==> ?p:R"; +by (REPEAT (resolve_tac (prems@[spec]) 1)) ; +qed "all_dupE"; (*** Negation rules, which translate between ~P and P-->False ***) @@ -107,24 +42,26 @@ (REPEAT (resolve_tac prems 1)) ]); (*This is useful with the special implication rules for each kind of P. *) -val not_to_imp = prove_goal IFOLP.thy - "[| p:~P; !!x. x:(P-->False) ==> q(x):Q |] ==> ?p:Q" - (fn prems=> [ (REPEAT (ares_tac (prems@[impI,notE]) 1)) ]); +val prems= Goal + "[| p:~P; !!x. x:(P-->False) ==> q(x):Q |] ==> ?p:Q"; +by (REPEAT (ares_tac (prems@[impI,notE]) 1)) ; +qed "not_to_imp"; (* For substitution int an assumption P, reduce Q to P-->Q, substitute into this implication, then apply impI to move P back into the assumptions. To specify P use something like eres_inst_tac [ ("P","ALL y. ?S(x,y)") ] rev_mp 1 *) -val rev_mp = prove_goal IFOLP.thy "[| p:P; q:P --> Q |] ==> ?p:Q" - (fn prems=> [ (REPEAT (resolve_tac (prems@[mp]) 1)) ]); +Goal "[| p:P; q:P --> Q |] ==> ?p:Q"; +by (REPEAT (ares_tac [mp] 1)) ; +qed "rev_mp"; (*Contrapositive of an inference rule*) -val contrapos = prove_goal IFOLP.thy "[| p:~Q; !!y. y:P==>q(y):Q |] ==> ?a:~P" - (fn [major,minor]=> - [ (rtac (major RS notE RS notI) 1), - (etac minor 1) ]); +val [major,minor]= Goal "[| p:~Q; !!y. y:P==>q(y):Q |] ==> ?a:~P"; +by (rtac (major RS notE RS notI) 1); +by (etac minor 1) ; +qed "contrapos"; (** Unique assumption tactic. Ignores proof objects. @@ -155,7 +92,7 @@ fun mp_tac i = eresolve_tac [notE,make_elim mp] i THEN assume_tac i; (*Like mp_tac but instantiates no variables*) -fun uniq_mp_tac i = eresolve_tac [notE,impE] i THEN uniq_assume_tac i; +fun int_uniq_mp_tac i = eresolve_tac [notE,impE] i THEN uniq_assume_tac i; (*** If-and-only-if ***) @@ -178,20 +115,20 @@ val iffD2 = prove_goalw IFOLP.thy [iff_def] "[| p:P <-> Q; q:Q |] ==> ?p:P" (fn prems => [ (rtac (conjunct2 RS mp) 1), (REPEAT (ares_tac prems 1)) ]); -val iff_refl = prove_goal IFOLP.thy "?p:P <-> P" - (fn _ => [ (REPEAT (ares_tac [iffI] 1)) ]); +Goal "?p:P <-> P"; +by (REPEAT (ares_tac [iffI] 1)) ; +qed "iff_refl"; -val iff_sym = prove_goal IFOLP.thy "p:Q <-> P ==> ?p:P <-> Q" - (fn [major] => - [ (rtac (major RS iffE) 1), - (rtac iffI 1), - (REPEAT (eresolve_tac [asm_rl,mp] 1)) ]); +Goal "p:Q <-> P ==> ?p:P <-> Q"; +by (etac iffE 1); +by (rtac iffI 1); +by (REPEAT (eresolve_tac [asm_rl,mp] 1)) ; +qed "iff_sym"; -val iff_trans = prove_goal IFOLP.thy "[| p:P <-> Q; q:Q<-> R |] ==> ?p:P <-> R" - (fn prems => - [ (cut_facts_tac prems 1), - (rtac iffI 1), - (REPEAT (eresolve_tac [asm_rl,iffE] 1 ORELSE mp_tac 1)) ]); +Goal "[| p:P <-> Q; q:Q<-> R |] ==> ?p:P <-> R"; +by (rtac iffI 1); +by (REPEAT (eresolve_tac [asm_rl,iffE] 1 ORELSE mp_tac 1)) ; +qed "iff_trans"; (*** Unique existence. NOTE THAT the following 2 quantifications @@ -200,17 +137,18 @@ do NOT mean the same thing. The parser treats EX!x y.P(x,y) as sequential. ***) -val ex1I = prove_goalw IFOLP.thy [ex1_def] - "[| p:P(a); !!x u. u:P(x) ==> f(u) : x=a |] ==> ?p:EX! x. P(x)" - (fn prems => [ (REPEAT (ares_tac (prems@[exI,conjI,allI,impI]) 1)) ]); +val prems = goalw IFOLP.thy [ex1_def] + "[| p:P(a); !!x u. u:P(x) ==> f(u) : x=a |] ==> ?p:EX! x. P(x)"; +by (REPEAT (ares_tac (prems@[exI,conjI,allI,impI]) 1)) ; +qed "ex1I"; -val ex1E = prove_goalw IFOLP.thy [ex1_def] +val prems = goalw IFOLP.thy [ex1_def] "[| p:EX! x. P(x); \ \ !!x u v. [| u:P(x); v:ALL y. P(y) --> y=x |] ==> f(x,u,v):R |] ==>\ -\ ?a : R" - (fn prems => - [ (cut_facts_tac prems 1), - (REPEAT (eresolve_tac [exE,conjE] 1 ORELSE ares_tac prems 1)) ]); +\ ?a : R"; +by (cut_facts_tac prems 1); +by (REPEAT (eresolve_tac [exE,conjE] 1 ORELSE ares_tac prems 1)) ; +qed "ex1E"; (*** <-> congruence rules for simplification ***) @@ -291,89 +229,83 @@ (fn [prem1,prem2] => [ rtac (prem2 RS rev_mp) 1, (rtac (prem1 RS ieqE) 1), rtac impI 1, atac 1 ]); -val sym = prove_goal IFOLP.thy "q:a=b ==> ?c:b=a" - (fn [major] => [ (rtac (major RS subst) 1), (rtac refl 1) ]); +Goal "q:a=b ==> ?c:b=a"; +by (etac subst 1); +by (rtac refl 1) ; +qed "sym"; -val trans = prove_goal IFOLP.thy "[| p:a=b; q:b=c |] ==> ?d:a=c" - (fn [prem1,prem2] => [ (rtac (prem2 RS subst) 1), (rtac prem1 1) ]); +Goal "[| p:a=b; q:b=c |] ==> ?d:a=c"; +by (etac subst 1 THEN assume_tac 1); +qed "trans"; (** ~ b=a ==> ~ a=b **) -val not_sym = prove_goal IFOLP.thy "p:~ b=a ==> ?q:~ a=b" - (fn [prem] => [ (rtac (prem RS contrapos) 1), (etac sym 1) ]); +Goal "p:~ b=a ==> ?q:~ a=b"; +by (etac contrapos 1); +by (etac sym 1) ; +qed "not_sym"; (*calling "standard" reduces maxidx to 0*) val ssubst = standard (sym RS subst); (*A special case of ex1E that would otherwise need quantifier expansion*) -val ex1_equalsE = prove_goal IFOLP.thy - "[| p:EX! x. P(x); q:P(a); r:P(b) |] ==> ?d:a=b" - (fn prems => - [ (cut_facts_tac prems 1), - (etac ex1E 1), - (rtac trans 1), - (rtac sym 2), - (REPEAT (eresolve_tac [asm_rl, spec RS mp] 1)) ]); +Goal "[| p:EX! x. P(x); q:P(a); r:P(b) |] ==> ?d:a=b"; +by (etac ex1E 1); +by (rtac trans 1); +by (rtac sym 2); +by (REPEAT (eresolve_tac [asm_rl, spec RS mp] 1)) ; +qed "ex1_equalsE"; (** Polymorphic congruence rules **) -val subst_context = prove_goal IFOLP.thy - "[| p:a=b |] ==> ?d:t(a)=t(b)" - (fn prems=> - [ (resolve_tac (prems RL [ssubst]) 1), - (rtac refl 1) ]); +Goal "[| p:a=b |] ==> ?d:t(a)=t(b)"; +by (etac ssubst 1); +by (rtac refl 1) ; +qed "subst_context"; -val subst_context2 = prove_goal IFOLP.thy - "[| p:a=b; q:c=d |] ==> ?p:t(a,c)=t(b,d)" - (fn prems=> - [ (EVERY1 (map rtac ((prems RL [ssubst]) @ [refl]))) ]); +Goal "[| p:a=b; q:c=d |] ==> ?p:t(a,c)=t(b,d)"; +by (REPEAT (etac ssubst 1)); +by (rtac refl 1) ; +qed "subst_context2"; -val subst_context3 = prove_goal IFOLP.thy - "[| p:a=b; q:c=d; r:e=f |] ==> ?p:t(a,c,e)=t(b,d,f)" - (fn prems=> - [ (EVERY1 (map rtac ((prems RL [ssubst]) @ [refl]))) ]); +Goal "[| p:a=b; q:c=d; r:e=f |] ==> ?p:t(a,c,e)=t(b,d,f)"; +by (REPEAT (etac ssubst 1)); +by (rtac refl 1) ; +qed "subst_context3"; (*Useful with eresolve_tac for proving equalties from known equalities. a = b | | c = d *) -val box_equals = prove_goal IFOLP.thy - "[| p:a=b; q:a=c; r:b=d |] ==> ?p:c=d" - (fn prems=> - [ (rtac trans 1), - (rtac trans 1), - (rtac sym 1), - (REPEAT (resolve_tac prems 1)) ]); +Goal "[| p:a=b; q:a=c; r:b=d |] ==> ?p:c=d"; +by (rtac trans 1); +by (rtac trans 1); +by (rtac sym 1); +by (REPEAT (assume_tac 1)) ; +qed "box_equals"; (*Dual of box_equals: for proving equalities backwards*) -val simp_equals = prove_goal IFOLP.thy - "[| p:a=c; q:b=d; r:c=d |] ==> ?p:a=b" - (fn prems=> - [ (rtac trans 1), - (rtac trans 1), - (REPEAT (resolve_tac (prems @ (prems RL [sym])) 1)) ]); +Goal "[| p:a=c; q:b=d; r:c=d |] ==> ?p:a=b"; +by (rtac trans 1); +by (rtac trans 1); +by (REPEAT (eresolve_tac [asm_rl, sym] 1)) ; +qed "simp_equals"; (** Congruence rules for predicate letters **) -val pred1_cong = prove_goal IFOLP.thy - "p:a=a' ==> ?p:P(a) <-> P(a')" - (fn prems => - [ (cut_facts_tac prems 1), - (rtac iffI 1), - (DEPTH_SOLVE (eresolve_tac [asm_rl, subst, ssubst] 1)) ]); +Goal "p:a=a' ==> ?p:P(a) <-> P(a')"; +by (rtac iffI 1); +by (DEPTH_SOLVE (eresolve_tac [asm_rl, subst, ssubst] 1)) ; +qed "pred1_cong"; -val pred2_cong = prove_goal IFOLP.thy - "[| p:a=a'; q:b=b' |] ==> ?p:P(a,b) <-> P(a',b')" - (fn prems => - [ (cut_facts_tac prems 1), - (rtac iffI 1), - (DEPTH_SOLVE (eresolve_tac [asm_rl, subst, ssubst] 1)) ]); +Goal "[| p:a=a'; q:b=b' |] ==> ?p:P(a,b) <-> P(a',b')"; +by (rtac iffI 1); +by (DEPTH_SOLVE (eresolve_tac [asm_rl, subst, ssubst] 1)) ; +qed "pred2_cong"; -val pred3_cong = prove_goal IFOLP.thy - "[| p:a=a'; q:b=b'; r:c=c' |] ==> ?p:P(a,b,c) <-> P(a',b',c')" - (fn prems => - [ (cut_facts_tac prems 1), - (rtac iffI 1), - (DEPTH_SOLVE (eresolve_tac [asm_rl, subst, ssubst] 1)) ]); +Goal "[| p:a=a'; q:b=b'; r:c=c' |] ==> ?p:P(a,b,c) <-> P(a',b',c')"; +by (rtac iffI 1); +by (DEPTH_SOLVE (eresolve_tac [asm_rl, subst, ssubst] 1)) ; +qed "pred3_cong"; (*special cases for free variables P, Q, R, S -- up to 3 arguments*) @@ -394,51 +326,46 @@ R. Dyckhoff, Contraction-free sequent calculi for intuitionistic logic (preprint, University of St Andrews, 1991) ***) -val conj_impE = prove_goal IFOLP.thy - "[| p:(P&Q)-->S; !!x. x:P-->(Q-->S) ==> q(x):R |] ==> ?p:R" - (fn major::prems=> - [ (REPEAT (ares_tac ([conjI, impI, major RS mp]@prems) 1)) ]); +val major::prems= Goal + "[| p:(P&Q)-->S; !!x. x:P-->(Q-->S) ==> q(x):R |] ==> ?p:R"; +by (REPEAT (ares_tac ([conjI, impI, major RS mp]@prems) 1)) ; +qed "conj_impE"; -val disj_impE = prove_goal IFOLP.thy - "[| p:(P|Q)-->S; !!x y.[| x:P-->S; y:Q-->S |] ==> q(x,y):R |] ==> ?p:R" - (fn major::prems=> - [ (DEPTH_SOLVE (ares_tac ([disjI1, disjI2, impI, major RS mp]@prems) 1)) ]); +val major::prems= Goal + "[| p:(P|Q)-->S; !!x y.[| x:P-->S; y:Q-->S |] ==> q(x,y):R |] ==> ?p:R"; +by (DEPTH_SOLVE (ares_tac ([disjI1, disjI2, impI, major RS mp]@prems) 1)) ; +qed "disj_impE"; (*Simplifies the implication. Classical version is stronger. Still UNSAFE since Q must be provable -- backtracking needed. *) -val imp_impE = prove_goal IFOLP.thy +val major::prems= Goal "[| p:(P-->Q)-->S; !!x y.[| x:P; y:Q-->S |] ==> q(x,y):Q; !!x. x:S ==> r(x):R |] ==> \ -\ ?p:R" - (fn major::prems=> - [ (REPEAT (ares_tac ([impI, major RS mp]@prems) 1)) ]); +\ ?p:R"; +by (REPEAT (ares_tac ([impI, major RS mp]@prems) 1)) ; +qed "imp_impE"; (*Simplifies the implication. Classical version is stronger. Still UNSAFE since ~P must be provable -- backtracking needed. *) -val not_impE = prove_goal IFOLP.thy - "[| p:~P --> S; !!y. y:P ==> q(y):False; !!y. y:S ==> r(y):R |] ==> ?p:R" - (fn major::prems=> - [ (REPEAT (ares_tac ([notI, impI, major RS mp]@prems) 1)) ]); +val major::prems= Goal + "[| p:~P --> S; !!y. y:P ==> q(y):False; !!y. y:S ==> r(y):R |] ==> ?p:R"; +by (REPEAT (ares_tac ([notI, impI, major RS mp]@prems) 1)) ; +qed "not_impE"; (*Simplifies the implication. UNSAFE. *) -val iff_impE = prove_goal IFOLP.thy +val major::prems= Goal "[| p:(P<->Q)-->S; !!x y.[| x:P; y:Q-->S |] ==> q(x,y):Q; \ -\ !!x y.[| x:Q; y:P-->S |] ==> r(x,y):P; !!x. x:S ==> s(x):R |] ==> ?p:R" - (fn major::prems=> - [ (REPEAT (ares_tac ([iffI, impI, major RS mp]@prems) 1)) ]); +\ !!x y.[| x:Q; y:P-->S |] ==> r(x,y):P; !!x. x:S ==> s(x):R |] ==> ?p:R"; +by (REPEAT (ares_tac ([iffI, impI, major RS mp]@prems) 1)) ; +qed "iff_impE"; (*What if (ALL x.~~P(x)) --> ~~(ALL x.P(x)) is an assumption? UNSAFE*) -val all_impE = prove_goal IFOLP.thy - "[| p:(ALL x. P(x))-->S; !!x. q:P(x); !!y. y:S ==> r(y):R |] ==> ?p:R" - (fn major::prems=> - [ (REPEAT (ares_tac ([allI, impI, major RS mp]@prems) 1)) ]); +val major::prems= Goal + "[| p:(ALL x. P(x))-->S; !!x. q:P(x); !!y. y:S ==> r(y):R |] ==> ?p:R"; +by (REPEAT (ares_tac ([allI, impI, major RS mp]@prems) 1)) ; +qed "all_impE"; (*Unsafe: (EX x.P(x))-->S is equivalent to ALL x.P(x)-->S. *) -val ex_impE = prove_goal IFOLP.thy - "[| p:(EX x. P(x))-->S; !!y. y:P(a)-->S ==> q(y):R |] ==> ?p:R" - (fn major::prems=> - [ (REPEAT (ares_tac ([exI, impI, major RS mp]@prems) 1)) ]); - -end; - -open IFOLP_Lemmas; - +val major::prems= Goal + "[| p:(EX x. P(x))-->S; !!y. y:P(a)-->S ==> q(y):R |] ==> ?p:R"; +by (REPEAT (ares_tac ([exI, impI, major RS mp]@prems) 1)) ; +qed "ex_impE"; diff -r 8baf94ddb345 -r 53e09e592278 src/FOLP/intprover.ML --- a/src/FOLP/intprover.ML Thu Jul 06 12:27:37 2000 +0200 +++ b/src/FOLP/intprover.ML Thu Jul 06 13:11:32 2000 +0200 @@ -54,7 +54,7 @@ (*Attack subgoals using safe inferences*) val safe_step_tac = FIRST' [uniq_assume_tac, - IFOLP_Lemmas.uniq_mp_tac, + int_uniq_mp_tac, biresolve_tac safe0_brls, hyp_subst_tac, biresolve_tac safep_brls] ;