diff -r b482d827899c -r 0a0e0dbe1269 src/HOL/Isar_examples/Cantor.thy --- a/src/HOL/Isar_examples/Cantor.thy Sat Sep 04 21:12:15 1999 +0200 +++ b/src/HOL/Isar_examples/Cantor.thy Sat Sep 04 21:13:01 1999 +0200 @@ -34,25 +34,25 @@ theorem "EX S. S ~: range(f :: 'a => 'a set)"; proof; - let ??S = "{x. x ~: f x}"; - show "??S ~: range f"; + let ?S = "{x. x ~: f x}"; + show "?S ~: range f"; proof; - assume "??S : range f"; + assume "?S : range f"; then; show False; proof; fix y; - assume "??S = f y"; - then; show ??thesis; + assume "?S = f y"; + then; show ?thesis; proof (rule equalityCE); - assume y_in_S: "y : ??S"; + assume y_in_S: "y : ?S"; assume y_in_fy: "y : f y"; from y_in_S; have y_notin_fy: "y ~: f y"; ..; - from y_notin_fy y_in_fy; show ??thesis; by contradiction; + from y_notin_fy y_in_fy; show ?thesis; by contradiction; next; - assume y_notin_S: "y ~: ??S"; + assume y_notin_S: "y ~: ?S"; assume y_notin_fy: "y ~: f y"; from y_notin_S; have y_in_fy: "y : f y"; ..; - from y_notin_fy y_in_fy; show ??thesis; by contradiction; + from y_notin_fy y_in_fy; show ?thesis; by contradiction; qed; qed; qed; @@ -67,23 +67,23 @@ theorem "EX S. S ~: range(f :: 'a => 'a set)"; proof; - let ??S = "{x. x ~: f x}"; - show "??S ~: range f"; + let ?S = "{x. x ~: f x}"; + show "?S ~: range f"; proof; - assume "??S : range f"; + assume "?S : range f"; thus False; proof; fix y; - assume "??S = f y"; - thus ??thesis; + assume "?S = f y"; + thus ?thesis; proof (rule equalityCE); assume "y : f y"; - assume "y : ??S"; hence "y ~: f y"; ..; - thus ??thesis; by contradiction; + assume "y : ?S"; hence "y ~: f y"; ..; + thus ?thesis; by contradiction; next; assume "y ~: f y"; - assume "y ~: ??S"; hence "y : f y"; ..; - thus ??thesis; by contradiction; + assume "y ~: ?S"; hence "y : f y"; ..; + thus ?thesis; by contradiction; qed; qed; qed;