diff -r a6cb18a25cbb -r f599984ec4c2 src/ZF/Rel.ML --- a/src/ZF/Rel.ML Fri Jun 21 18:40:06 2002 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,55 +0,0 @@ -(* Title: ZF/Rel.ML - ID: $Id$ - Author: Lawrence C Paulson, Cambridge University Computer Laboratory - Copyright 1994 University of Cambridge - -Relations in Zermelo-Fraenkel Set Theory -*) - -(*** Some properties of relations -- useful? ***) - -(* irreflexivity *) - -val prems = Goalw [irrefl_def] - "[| !!x. x:A ==> ~: r |] ==> irrefl(A,r)"; -by (REPEAT (ares_tac (prems @ [ballI]) 1)); -qed "irreflI"; - -Goalw [irrefl_def] "[| irrefl(A,r); x:A |] ==> ~: r"; -by (Blast_tac 1); -qed "irreflE"; - -(* symmetry *) - -val prems = Goalw [sym_def] - "[| !!x y.: r ==> : r |] ==> sym(r)"; -by (REPEAT (ares_tac (prems @ [allI,impI]) 1)); -qed "symI"; - -Goalw [sym_def] "[| sym(r); : r |] ==> : r"; -by (Blast_tac 1); -qed "symE"; - -(* antisymmetry *) - -val prems = Goalw [antisym_def] - "[| !!x y.[| : r; : r |] ==> x=y |] ==> \ -\ antisym(r)"; -by (REPEAT (ares_tac (prems @ [allI,impI]) 1)); -qed "antisymI"; - -Goalw [antisym_def] "[| antisym(r); : r; : r |] ==> x=y"; -by (Blast_tac 1); -qed "antisymE"; - -(* transitivity *) - -Goalw [trans_def] "[| trans(r); :r; :r |] ==> :r"; -by (Blast_tac 1); -qed "transD"; - -Goalw [trans_on_def] - "[| trans[A](r); :r; :r; a:A; b:A; c:A |] ==> :r"; -by (Blast_tac 1); -qed "trans_onD"; -