author traytel Thu, 20 Feb 2014 13:53:26 +0100 changeset 55603 48596c45bf7f parent 55602 257bd115fcca child 55604 42e4e8c2e8dc
less flex-flex pairs (thanks to Lars' statistics)
```--- a/src/HOL/BNF_Cardinal_Order_Relation.thy	Thu Feb 20 11:40:03 2014 +0100
+++ b/src/HOL/BNF_Cardinal_Order_Relation.thy	Thu Feb 20 13:53:26 2014 +0100
@@ -414,7 +414,7 @@
let ?h = "\<lambda> b'::'b. if b' = b then a else undefined"
have "inj_on ?h {b} \<and> ?h ` {b} \<le> A"
using * unfolding inj_on_def by auto
-  thus ?thesis using card_of_ordLeq by fast
+  thus ?thesis unfolding card_of_ordLeq[symmetric] by (intro exI)
qed

corollary Card_order_singl_ordLeq:```
```--- a/src/HOL/BNF_Constructions_on_Wellorders.thy	Thu Feb 20 11:40:03 2014 +0100
+++ b/src/HOL/BNF_Constructions_on_Wellorders.thy	Thu Feb 20 13:53:26 2014 +0100
@@ -1652,8 +1652,7 @@
qed(insert h, unfold Func_def Func_map_def, auto)
qed
moreover have "g \<in> Func A2 A1" unfolding g_def apply(rule Func_map[OF h])
-    using inv_into_into j2A2 B1 A2 inv_into_into
-    unfolding j1_def image_def by fast+
+    using j2A2 B1 A2 unfolding j1_def image_def by (fast intro: inv_into_into)+
ultimately show "h \<in> Func_map B2 f1 f2 ` Func A2 A1"
unfolding Func_map_def[abs_def] unfolding image_def by auto
qed(insert B1 Func_map[OF _ _ A2(2)], auto)```