diff -r f552152d7747 -r 46cfc4b8112e src/HOL/Set.thy --- a/src/HOL/Set.thy Wed Mar 17 19:37:44 2010 +0100 +++ b/src/HOL/Set.thy Thu Mar 18 12:58:52 2010 +0100 @@ -462,7 +462,7 @@ unfolding mem_def by (erule le_funE, erule le_boolE) -- {* Rule in Modus Ponens style. *} -lemma rev_subsetD [noatp,intro?]: "c \ A ==> A \ B ==> c \ B" +lemma rev_subsetD [no_atp,intro?]: "c \ A ==> A \ B ==> c \ B" -- {* The same, with reversed premises for use with @{text erule} -- cf @{text rev_mp}. *} by (rule subsetD) @@ -471,13 +471,13 @@ \medskip Converts @{prop "A \ B"} to @{prop "x \ A ==> x \ B"}. *} -lemma subsetCE [noatp,elim]: "A \ B ==> (c \ A ==> P) ==> (c \ B ==> P) ==> P" +lemma subsetCE [no_atp,elim]: "A \ B ==> (c \ A ==> P) ==> (c \ B ==> P) ==> P" -- {* Classical elimination rule. *} unfolding mem_def by (blast dest: le_funE le_boolE) -lemma subset_eq [noatp]: "A \ B = (\x\A. x \ B)" by blast +lemma subset_eq [no_atp]: "A \ B = (\x\A. x \ B)" by blast -lemma contra_subsetD [noatp]: "A \ B ==> c \ B ==> c \ A" +lemma contra_subsetD [no_atp]: "A \ B ==> c \ B ==> c \ A" by blast lemma subset_refl [simp]: "A \ A" @@ -791,11 +791,11 @@ subsubsection {* Singletons, using insert *} -lemma singletonI [intro!,noatp]: "a : {a}" +lemma singletonI [intro!,no_atp]: "a : {a}" -- {* Redundant? But unlike @{text insertCI}, it proves the subgoal immediately! *} by (rule insertI1) -lemma singletonD [dest!,noatp]: "b : {a} ==> b = a" +lemma singletonD [dest!,no_atp]: "b : {a} ==> b = a" by blast lemmas singletonE = singletonD [elim_format] @@ -806,11 +806,11 @@ lemma singleton_inject [dest!]: "{a} = {b} ==> a = b" by blast -lemma singleton_insert_inj_eq [iff,noatp]: +lemma singleton_insert_inj_eq [iff,no_atp]: "({b} = insert a A) = (a = b & A \ {b})" by blast -lemma singleton_insert_inj_eq' [iff,noatp]: +lemma singleton_insert_inj_eq' [iff,no_atp]: "(insert a A = {b}) = (a = b & A \ {b})" by blast @@ -837,7 +837,7 @@ *} definition image :: "('a => 'b) => 'a set => 'b set" (infixr "`" 90) where - image_def [noatp]: "f ` A = {y. EX x:A. y = f(x)}" + image_def [no_atp]: "f ` A = {y. EX x:A. y = f(x)}" abbreviation range :: "('a => 'b) => 'b set" where -- "of function" @@ -942,10 +942,10 @@ subsubsection {* The ``proper subset'' relation *} -lemma psubsetI [intro!,noatp]: "A \ B ==> A \ B ==> A \ B" +lemma psubsetI [intro!,no_atp]: "A \ B ==> A \ B ==> A \ B" by (unfold less_le) blast -lemma psubsetE [elim!,noatp]: +lemma psubsetE [elim!,no_atp]: "[|A \ B; [|A \ B; ~ (B\A)|] ==> R|] ==> R" by (unfold less_le) blast @@ -1102,12 +1102,12 @@ lemma insert_inter_insert[simp]: "insert a A \ insert a B = insert a (A \ B)" by blast -lemma insert_disjoint [simp,noatp]: +lemma insert_disjoint [simp,no_atp]: "(insert a A \ B = {}) = (a \ B \ A \ B = {})" "({} = insert a A \ B) = (a \ B \ {} = A \ B)" by auto -lemma disjoint_insert [simp,noatp]: +lemma disjoint_insert [simp,no_atp]: "(B \ insert a A = {}) = (a \ B \ B \ A = {})" "({} = A \ insert b B) = (b \ A \ {} = A \ B)" by auto @@ -1139,7 +1139,7 @@ by blast -lemma image_Collect [noatp]: "f ` {x. P x} = {f x | x. P x}" +lemma image_Collect [no_atp]: "f ` {x. P x} = {f x | x. P x}" -- {* NOT suitable as a default simprule: the RHS isn't simpler than the LHS, with its implicit quantifier and conjunction. Also image enjoys better equational properties than does the RHS. *} @@ -1156,7 +1156,7 @@ text {* \medskip @{text range}. *} -lemma full_SetCompr_eq [noatp]: "{u. \x. u = f x} = range f" +lemma full_SetCompr_eq [no_atp]: "{u. \x. u = f x} = range f" by auto lemma range_composition: "range (\x. f (g x)) = f`range g" @@ -1213,7 +1213,7 @@ lemma Int_Un_distrib2: "(B \ C) \ A = (B \ A) \ (C \ A)" by blast -lemma Int_UNIV [simp,noatp]: "(A \ B = UNIV) = (A = UNIV & B = UNIV)" +lemma Int_UNIV [simp,no_atp]: "(A \ B = UNIV) = (A = UNIV & B = UNIV)" by blast lemma Int_subset_iff [simp]: "(C \ A \ B) = (C \ A & C \ B)" @@ -1376,7 +1376,7 @@ lemma Diff_eq: "A - B = A \ (-B)" by blast -lemma Diff_eq_empty_iff [simp,noatp]: "(A - B = {}) = (A \ B)" +lemma Diff_eq_empty_iff [simp,no_atp]: "(A - B = {}) = (A \ B)" by blast lemma Diff_cancel [simp]: "A - A = {}" @@ -1397,7 +1397,7 @@ lemma Diff_UNIV [simp]: "A - UNIV = {}" by blast -lemma Diff_insert0 [simp,noatp]: "x \ A ==> A - insert x B = A - B" +lemma Diff_insert0 [simp,no_atp]: "x \ A ==> A - insert x B = A - B" by blast lemma Diff_insert: "A - insert a B = A - B - {a}" @@ -1639,7 +1639,7 @@ -- {* monotonicity *} by blast -lemma vimage_image_eq [noatp]: "f -` (f ` A) = {y. EX x:A. f x = f y}" +lemma vimage_image_eq [no_atp]: "f -` (f ` A) = {y. EX x:A. f x = f y}" by (blast intro: sym) lemma image_vimage_subset: "f ` (f -` A) <= A"