# HG changeset patch # User berghofe # Date 1173540292 -3600 # Node ID 28344ccffc35a121bf7270271c98a9e6752d7705 # Parent 6a56bf1b3a64997fa8d2f2eca9a854a294789ab5 Adapted to changes in definition of SUP. diff -r 6a56bf1b3a64 -r 28344ccffc35 src/HOL/Library/Continuity.thy --- a/src/HOL/Library/Continuity.thy Sat Mar 10 16:23:28 2007 +0100 +++ b/src/HOL/Library/Continuity.thy Sat Mar 10 16:24:52 2007 +0100 @@ -16,7 +16,7 @@ "chain M \ (\i. M i \ M (Suc i))" definition - continuous :: "('a::order \ 'a::order) \ bool" where + continuous :: "('a::comp_lat \ 'a::comp_lat) \ bool" where "continuous F \ (\M. chain M \ F (SUP i. M i) = (SUP i. F (M i)))" abbreviation @@ -24,12 +24,12 @@ "bot \ Sup {}" lemma SUP_nat_conv: - "(SUP n::nat. M n::'a::comp_lat) = sup (M 0) (SUP n. M(Suc n))" + "(SUP n. M n) = sup (M 0) (SUP n. M(Suc n))" apply(rule order_antisym) apply(rule SUP_leI) apply(case_tac n) apply simp - apply (blast intro:le_SUPI le_supI2) + apply (fast intro:le_SUPI le_supI2) apply(simp) apply (blast intro:SUP_leI le_SUPI) done @@ -43,10 +43,10 @@ have "F B = sup (F A) (F B)" proof - have "sup A B = B" using `A <= B` by (simp add:sup_absorb2) - hence "F B = F(SUP i. ?C i)" by(simp add: SUP_nat_conv) + hence "F B = F(SUP i. ?C i)" by (subst SUP_nat_conv) simp also have "\ = (SUP i. F(?C i))" using `chain ?C` `continuous F` by(simp add:continuous_def) - also have "\ = sup (F A) (F B)" by(simp add: SUP_nat_conv) + also have "\ = sup (F A) (F B)" by (subst SUP_nat_conv) simp finally show ?thesis . qed thus "F A \ F B" by(subst le_iff_sup, simp) @@ -80,7 +80,7 @@ thus ?thesis by(auto simp add:chain_def) qed hence "F ?U = (SUP i. (F^(i+1)) bot)" using `continuous F` by (simp add:continuous_def) - also have "\ \ ?U" by(blast intro:SUP_leI le_SUPI) + also have "\ \ ?U" by(fast intro:SUP_leI le_SUPI) finally show "F ?U \ ?U" . qed ultimately show ?thesis by (blast intro:order_antisym) diff -r 6a56bf1b3a64 -r 28344ccffc35 src/HOL/Library/Graphs.thy --- a/src/HOL/Library/Graphs.thy Sat Mar 10 16:23:28 2007 +0100 +++ b/src/HOL/Library/Graphs.thy Sat Mar 10 16:24:52 2007 +0100 @@ -245,7 +245,7 @@ lemma Sup_graph_eq: "(SUP n. Graph (G n)) = Graph (\n. G n)" - unfolding SUP_def + unfolding SUPR_def apply (rule order_antisym) apply (rule Sup_least) apply auto diff -r 6a56bf1b3a64 -r 28344ccffc35 src/HOL/Library/Kleene_Algebras.thy --- a/src/HOL/Library/Kleene_Algebras.thy Sat Mar 10 16:23:28 2007 +0100 +++ b/src/HOL/Library/Kleene_Algebras.thy Sat Mar 10 16:24:52 2007 +0100 @@ -104,7 +104,7 @@ assumes "l \ M i" shows "l \ (SUP i. M i)" using prems - by (rule order_trans) (rule le_SUPI, rule refl) + by (rule order_trans) (rule le_SUPI [OF UNIV_I]) lemma zero_minimum[simp]: "(0::'a::pre_kleene) \ x" @@ -117,21 +117,20 @@ have [simp]: "1 \ star a" unfolding star_cont[of 1 a 1, simplified] - by (rule le_SUPI) (rule power_0[symmetric]) + by (subst power_0[symmetric]) (rule le_SUPI [OF UNIV_I]) show "1 + a * star a \ star a" apply (rule plus_leI, simp) apply (simp add:star_cont[of a a 1, simplified]) apply (simp add:star_cont[of 1 a 1, simplified]) - apply (intro SUP_leI le_SUPI) - by (rule power_Suc[symmetric]) + apply (subst power_Suc[symmetric]) + by (intro SUP_leI le_SUPI UNIV_I) show "1 + star a * a \ star a" apply (rule plus_leI, simp) apply (simp add:star_cont[of 1 a a, simplified]) apply (simp add:star_cont[of 1 a 1, simplified]) - apply (intro SUP_leI le_SUPI) - by (simp add:power_Suc[symmetric] power_commutes) + by (auto intro: SUP_leI le_SUPI UNIV_I simp add: power_Suc[symmetric] power_commutes) show "a * x \ x \ star a * x \ x" proof -