src/ZF/ex/CoUnit.thy
changeset 46822 95f1e700b712
parent 42793 88bee9f6eec7
child 58871 c399ae4b836f
--- a/src/ZF/ex/CoUnit.thy	Tue Mar 06 16:06:52 2012 +0000
+++ b/src/ZF/ex/CoUnit.thy	Tue Mar 06 16:46:27 2012 +0000
@@ -27,7 +27,7 @@
 inductive_cases ConE: "Con(x) \<in> counit"
   -- {* USELESS because folding on @{term "Con(xa) == xa"} fails. *}
 
-lemma Con_iff: "Con(x) = Con(y) <-> x = y"
+lemma Con_iff: "Con(x) = Con(y) \<longleftrightarrow> x = y"
   -- {* Proving freeness results. *}
   by (auto elim!: counit.free_elims)
 
@@ -55,7 +55,7 @@
 
 inductive_cases Con2E: "Con2(x, y) \<in> counit2"
 
-lemma Con2_iff: "Con2(x, y) = Con2(x', y') <-> x = x' & y = y'"
+lemma Con2_iff: "Con2(x, y) = Con2(x', y') \<longleftrightarrow> x = x' & y = y'"
   -- {* Proving freeness results. *}
   by (fast elim!: counit2.free_elims)
 
@@ -73,7 +73,7 @@
   done
 
 lemma counit2_Int_Vset_subset [rule_format]:
-  "Ord(i) ==> \<forall>x y. x \<in> counit2 --> y \<in> counit2 --> x Int Vset(i) \<subseteq> y"
+  "Ord(i) ==> \<forall>x y. x \<in> counit2 \<longrightarrow> y \<in> counit2 \<longrightarrow> x \<inter> Vset(i) \<subseteq> y"
   -- {* Lemma for proving finality. *}
   apply (erule trans_induct)
   apply (tactic "safe_tac (put_claset subset_cs @{context})")