# HG changeset patch
# User blanchet
# Date 1347438956 -7200
# Node ID 340844cbf7af15e990286ab20f2e7fcd6768e284
# Parent  a1b0654e7c90cbf5e8d6afaaecabab00e1a17e3e
tuning

diff -r a1b0654e7c90 -r 340844cbf7af src/HOL/Codatatype/BNF_Def.thy
--- a/src/HOL/Codatatype/BNF_Def.thy	Wed Sep 12 10:18:31 2012 +0200
+++ b/src/HOL/Codatatype/BNF_Def.thy	Wed Sep 12 10:35:56 2012 +0200
@@ -51,7 +51,7 @@
   moreover have "f1 (fst a') = f2 (snd a')"
   using a' unfolding csquare_def thePull_def by auto
   ultimately show "\<exists> ja'. ?phi a' ja'"
-  using assms unfolding wppull_def by auto
+  using assms unfolding wppull_def by blast
 qed
 
 lemma wpull_wppull:
@@ -64,7 +64,7 @@
   then obtain a' where a': "a' \<in> A'" and b1: "b1 = p1' a'" and b2: "b2 = p2' a'"
   using wp unfolding wpull_def by blast
   show "\<exists>a\<in>A. e1 (p1 a) = e1 b1 \<and> e2 (p2 a) = e2 b2"
-  apply(rule bexI[of _ "j a'"]) unfolding b1 b2 using a' 1 by auto
+  apply (rule bexI[of _ "j a'"]) unfolding b1 b2 using a' 1 by auto
 qed
 
 lemma wppull_id: "\<lbrakk>wpull UNIV UNIV UNIV f1 f2 p1 p2; e1 = id; e2 = id\<rbrakk> \<Longrightarrow>
@@ -87,8 +87,7 @@
 definition "pick_middle P Q a c = (SOME b. (a,b) \<in> P \<and> (b,c) \<in> Q)"
 
 lemma pick_middle:
-assumes "(a,c) \<in> P O Q"
-shows "(a, pick_middle P Q a c) \<in> P \<and> (pick_middle P Q a c, c) \<in> Q"
+"(a,c) \<in> P O Q \<Longrightarrow> (a, pick_middle P Q a c) \<in> P \<and> (pick_middle P Q a c, c) \<in> Q"
 unfolding pick_middle_def apply(rule someI_ex)
 using assms unfolding relcomp_def by auto
 
@@ -96,7 +95,8 @@
 definition sndO where "sndO P Q ac = (pick_middle P Q (fst ac) (snd ac), snd ac)"
 
 lemma fstO_in: "ac \<in> P O Q \<Longrightarrow> fstO P Q ac \<in> P"
-by (metis assms fstO_def pick_middle surjective_pairing)
+unfolding fstO_def
+by (subst (asm) surjective_pairing) (rule pick_middle[THEN conjunct1])
 
 lemma fst_fstO: "fst bc = (fst \<circ> fstO P Q) bc"
 unfolding comp_def fstO_def by simp
@@ -105,11 +105,12 @@
 unfolding comp_def sndO_def by simp
 
 lemma sndO_in: "ac \<in> P O Q \<Longrightarrow> sndO P Q ac \<in> Q"
-by (metis assms sndO_def pick_middle surjective_pairing)
+unfolding sndO_def
+by (subst (asm) surjective_pairing) (rule pick_middle[THEN conjunct2])
 
 lemma csquare_fstO_sndO:
 "csquare (P O Q) snd fst (fstO P Q) (sndO P Q)"
-unfolding csquare_def fstO_def sndO_def using pick_middle by auto
+unfolding csquare_def fstO_def sndO_def using pick_middle by simp
 
 lemma wppull_fstO_sndO:
 shows "wppull (P O Q) P Q snd fst fst snd (fstO P Q) (sndO P Q)"
diff -r a1b0654e7c90 -r 340844cbf7af src/HOL/Codatatype/BNF_FP.thy
--- a/src/HOL/Codatatype/BNF_FP.thy	Wed Sep 12 10:18:31 2012 +0200
+++ b/src/HOL/Codatatype/BNF_FP.thy	Wed Sep 12 10:35:56 2012 +0200
@@ -80,16 +80,24 @@
 lemma obj_one_pointE: "\<forall>x. s = x \<longrightarrow> P \<Longrightarrow> P"
 by blast
 
+lemma obj_sumE_f':
+"\<lbrakk>\<forall>x. s = f (Inl x) \<longrightarrow> P; \<forall>x. s = f (Inr x) \<longrightarrow> P\<rbrakk> \<Longrightarrow> s = f x \<longrightarrow> P"
+by (cases x) blast+
+
 lemma obj_sumE_f:
 "\<lbrakk>\<forall>x. s = f (Inl x) \<longrightarrow> P; \<forall>x. s = f (Inr x) \<longrightarrow> P\<rbrakk> \<Longrightarrow> \<forall>x. s = f x \<longrightarrow> P"
-by (metis sum.exhaust)
+by (rule allI) (rule obj_sumE_f')
 
 lemma obj_sumE: "\<lbrakk>\<forall>x. s = Inl x \<longrightarrow> P; \<forall>x. s = Inr x \<longrightarrow> P\<rbrakk> \<Longrightarrow> P"
 by (cases s) auto
 
+lemma obj_sum_step':
+"\<lbrakk>\<forall>x. s = f (Inr (Inl x)) \<longrightarrow> P; \<forall>x. s = f (Inr (Inr x)) \<longrightarrow> P\<rbrakk> \<Longrightarrow> s = f (Inr x) \<longrightarrow> P"
+by (cases x) blast+
+
 lemma obj_sum_step:
-  "\<lbrakk>\<forall>x. s = f (Inr (Inl x)) \<longrightarrow> P; \<forall>x. s = f (Inr (Inr x)) \<longrightarrow> P\<rbrakk> \<Longrightarrow> \<forall>x. s = f (Inr x) \<longrightarrow> P"
-by (metis obj_sumE)
+"\<lbrakk>\<forall>x. s = f (Inr (Inl x)) \<longrightarrow> P; \<forall>x. s = f (Inr (Inr x)) \<longrightarrow> P\<rbrakk> \<Longrightarrow> \<forall>x. s = f (Inr x) \<longrightarrow> P"
+by (rule allI) (rule obj_sum_step')
 
 lemma sum_case_if:
 "sum_case f g (if p then Inl x else Inr y) = (if p then f x else g y)"
diff -r a1b0654e7c90 -r 340844cbf7af src/HOL/Codatatype/BNF_GFP.thy
--- a/src/HOL/Codatatype/BNF_GFP.thy	Wed Sep 12 10:18:31 2012 +0200
+++ b/src/HOL/Codatatype/BNF_GFP.thy	Wed Sep 12 10:35:56 2012 +0200
@@ -278,12 +278,10 @@
 
 (* pick according to the weak pullback *)
 definition pickWP_pred where
-"pickWP_pred A p1 p2 b1 b2 a \<equiv>
- a \<in> A \<and> p1 a = b1 \<and> p2 a = b2"
+"pickWP_pred A p1 p2 b1 b2 a \<equiv> a \<in> A \<and> p1 a = b1 \<and> p2 a = b2"
 
 definition pickWP where
-"pickWP A p1 p2 b1 b2 \<equiv>
- SOME a. pickWP_pred A p1 p2 b1 b2 a"
+"pickWP A p1 p2 b1 b2 \<equiv> SOME a. pickWP_pred A p1 p2 b1 b2 a"
 
 lemma pickWP_pred:
 assumes "wpull A B1 B2 f1 f2 p1 p2" and
diff -r a1b0654e7c90 -r 340844cbf7af src/HOL/Codatatype/Tools/bnf_def.ML
--- a/src/HOL/Codatatype/Tools/bnf_def.ML	Wed Sep 12 10:18:31 2012 +0200
+++ b/src/HOL/Codatatype/Tools/bnf_def.ML	Wed Sep 12 10:35:56 2012 +0200
@@ -482,7 +482,6 @@
 val bd_CnotzeroN = "bd_Cnotzero";
 val collect_set_naturalN = "collect_set_natural";
 val in_bdN = "in_bd";
-val in_congN = "in_cong";
 val in_monoN = "in_mono";
 val in_relN = "in_rel";
 val map_idN = "map_id";
@@ -490,9 +489,7 @@
 val map_compN = "map_comp";
 val map_comp'N = "map_comp'";
 val map_congN = "map_cong";
-val map_wppullN = "map_wppull";
 val map_wpullN = "map_wpull";
-val rel_congN = "rel_cong";
 val rel_IdN = "rel_Id";
 val rel_GrN = "rel_Gr";
 val rel_converseN = "rel_converse";