# HG changeset patch # User paulson # Date 938524347 -7200 # Node ID dcb93b29568303c75c36666c3b30a3834ffe8d68 # Parent 4074bc1e380d16cad65d9ebff01be9e7fa6b4ba6 zero_is_mult, by symmetry diff -r 4074bc1e380d -r dcb93b295683 src/HOL/Arith.ML --- a/src/HOL/Arith.ML Tue Sep 28 14:24:22 1999 +0200 +++ b/src/HOL/Arith.ML Tue Sep 28 15:12:27 1999 +0200 @@ -336,7 +336,13 @@ by (induct_tac "n" 2); by (ALLGOALS Asm_simp_tac); qed "mult_is_0"; -Addsimps [mult_is_0]; + +Goal "(0 = m*n) = (0=m | 0=n)"; +by (cut_facts_tac [mult_is_0] 1); +by (full_simp_tac (simpset() addsimps [eq_commute]) 1); +qed "zero_is_mult"; + +Addsimps [mult_is_0, zero_is_mult]; Goal "m <= m*(m::nat)"; by (induct_tac "m" 1);