diff -r 70c6014c9b6f -r cebe01deba80 src/ZF/upair.ML --- a/src/ZF/upair.ML Thu Oct 07 09:49:46 1993 +0100 +++ b/src/ZF/upair.ML Thu Oct 07 10:48:16 1993 +0100 @@ -56,7 +56,7 @@ (fn _ => [ (fast_tac (lemmas_cs addIs [UnI1,UnI2] addSEs [UnE]) 1) ]); (*Classical introduction rule: no commitment to A vs B*) -val UnCI = prove_goal ZF.thy "(~c : B ==> c : A) ==> c : A Un B" +val UnCI = prove_goal ZF.thy "(c ~: B ==> c : A) ==> c : A Un B" (fn [prem]=> [ (rtac (disjCI RS (Un_iff RS iffD2)) 1), (etac prem 1) ]); @@ -91,7 +91,7 @@ (*** Rules for set difference -- defined via Upair ***) val DiffI = prove_goalw ZF.thy [Diff_def] - "[| c : A; ~ c : B |] ==> c : A - B" + "[| c : A; c ~: B |] ==> c : A - B" (fn prems=> [ (REPEAT (resolve_tac (prems @ [CollectI]) 1)) ]); val DiffD1 = prove_goalw ZF.thy [Diff_def] @@ -103,12 +103,12 @@ (fn [major,minor]=> [ (rtac (minor RS (major RS CollectD2 RS notE)) 1) ]); val DiffE = prove_goal ZF.thy - "[| c : A - B; [| c:A; ~ c:B |] ==> P |] ==> P" + "[| c : A - B; [| c:A; c~:B |] ==> P |] ==> P" (fn prems=> [ (resolve_tac prems 1), (REPEAT (ares_tac (prems RL [DiffD1, DiffD2 RS notI]) 1)) ]); -val Diff_iff = prove_goal ZF.thy "c : A-B <-> (c:A & ~ c:B)" +val Diff_iff = prove_goal ZF.thy "c : A-B <-> (c:A & c~:B)" (fn _ => [ (fast_tac (lemmas_cs addSIs [DiffI] addSEs [DiffE]) 1) ]); (*** Rules for cons -- defined via Un and Upair ***) @@ -129,7 +129,7 @@ (fn _ => [ (fast_tac (lemmas_cs addIs [consI1,consI2] addSEs [consE]) 1) ]); (*Classical introduction rule*) -val consCI = prove_goal ZF.thy "(~ a:B ==> a=b) ==> a: cons(b,B)" +val consCI = prove_goal ZF.thy "(a~:B ==> a=b) ==> a: cons(b,B)" (fn [prem]=> [ (rtac (disjCI RS (cons_iff RS iffD2)) 1), (etac prem 1) ]); @@ -223,7 +223,7 @@ val mem_anti_refl = prove_goal ZF.thy "a:a ==> P" (fn [major]=> [ (rtac (major RS (major RS mem_anti_sym)) 1) ]); -val mem_not_refl = prove_goal ZF.thy "~ a:a" +val mem_not_refl = prove_goal ZF.thy "a~:a" (K [ (rtac notI 1), (etac mem_anti_refl 1) ]); (*** Rules for succ ***) @@ -245,7 +245,7 @@ (fn _ => [ (fast_tac (lemmas_cs addIs [succI1,succI2] addSEs [succE]) 1) ]); (*Classical introduction rule*) -val succCI = prove_goal ZF.thy "(~ i:j ==> i=j) ==> i: succ(j)" +val succCI = prove_goal ZF.thy "(i~:j ==> i=j) ==> i: succ(j)" (fn [prem]=> [ (rtac (disjCI RS (succ_iff RS iffD2)) 1), (etac prem 1) ]); @@ -256,7 +256,7 @@ (rtac succI1 1) ]); (*Useful for rewriting*) -val succ_not_0 = prove_goal ZF.thy "~ succ(n)=0" +val succ_not_0 = prove_goal ZF.thy "succ(n) ~= 0" (fn _=> [ (rtac notI 1), (etac succ_neq_0 1) ]); (* succ(c) <= B ==> c : B *)