# HG changeset patch # User nipkow # Date 907259365 -7200 # Node ID 6b8dee1a6ebb8263d1cadfa24761be844e794f36 # Parent a12b25c53df11fac59c7b6369fdac655566bb808 a few new lemmas. diff -r a12b25c53df1 -r 6b8dee1a6ebb src/HOL/Arith.ML --- a/src/HOL/Arith.ML Thu Oct 01 18:28:47 1998 +0200 +++ b/src/HOL/Arith.ML Thu Oct 01 18:29:25 1998 +0200 @@ -93,11 +93,27 @@ (** Reasoning about m+0=0, etc. **) Goal "(m+n = 0) = (m=0 & n=0)"; -by (induct_tac "m" 1); -by (ALLGOALS Asm_simp_tac); +by (exhaust_tac "m" 1); +by (Auto_tac); qed "add_is_0"; AddIffs [add_is_0]; +Goal "(0 = m+n) = (m=0 & n=0)"; +by (exhaust_tac "m" 1); +by (Auto_tac); +qed "zero_is_add"; +AddIffs [zero_is_add]; + +Goal "(m+n=1) = (m=1 & n=0 | m=0 & n=1)"; +by(exhaust_tac "m" 1); +by(Auto_tac); +qed "add_is_1"; + +Goal "(1=m+n) = (m=1 & n=0 | m=0 & n=1)"; +by(exhaust_tac "m" 1); +by(Auto_tac); +qed "one_is_add"; + Goal "(0