src/HOL/Real/Lubs.ML
changeset 5148 74919e8f221c
parent 5143 b94cd208f073
child 7219 4e3f386c2e37
--- a/src/HOL/Real/Lubs.ML	Wed Jul 15 14:13:18 1998 +0200
+++ b/src/HOL/Real/Lubs.ML	Wed Jul 15 14:19:02 1998 +0200
@@ -42,12 +42,12 @@
 qed "leastPD3";
 
 Goalw [isLub_def,isUb_def,leastP_def] 
-      "!!x. isLub R S x ==> S *<= x";
+      "isLub R S x ==> S *<= x";
 by (Step_tac 1);
 qed "isLubD1";
 
 Goalw [isLub_def,isUb_def,leastP_def] 
-      "!!x. isLub R S x ==> x: R";
+      "isLub R S x ==> x: R";
 by (Step_tac 1);
 qed "isLubD1a";
 
@@ -68,7 +68,7 @@
 qed "isLubI1";
 
 Goalw [isLub_def,leastP_def] 
-      "!!x. [| isUb R S x; x <=* Collect (isUb R S) |] ==> isLub R S x";
+      "[| isUb R S x; x <=* Collect (isUb R S) |] ==> isLub R S x";
 by (Step_tac 1);
 qed "isLubI2";