# HG changeset patch # User paulson # Date 901636592 -7200 # Node ID a3f26b19cd7e642560b43178c47bc1c5da062c41 # Parent 6023540393069261b91f68d3ee99e68122296574 Tidied diff -r 602354039306 -r a3f26b19cd7e src/HOL/ex/NatSum.ML --- a/src/HOL/ex/NatSum.ML Tue Jul 28 16:33:43 1998 +0200 +++ b/src/HOL/ex/NatSum.ML Tue Jul 28 16:36:32 1998 +0200 @@ -19,16 +19,14 @@ by (Asm_simp_tac 1); qed "sum_of_naturals"; -Goal - "Suc(Suc(Suc(Suc 2)))*sum (%i. i*i) (Suc n) = n*Suc(n)*Suc(2*n)"; +Goal "Suc(Suc(Suc(Suc 2)))*sum (%i. i*i) (Suc n) = n*Suc(n)*Suc(2*n)"; by (Simp_tac 1); by (induct_tac "n" 1); by (Simp_tac 1); by (Asm_simp_tac 1); qed "sum_of_squares"; -Goal - "Suc(Suc 2)*sum (%i. i*i*i) (Suc n) = n*n*Suc(n)*Suc(n)"; +Goal "Suc(Suc 2)*sum (%i. i*i*i) (Suc n) = n*n*Suc(n)*Suc(n)"; by (Simp_tac 1); by (induct_tac "n" 1); by (Simp_tac 1);