# HG changeset patch # User huffman # Date 1176688935 -7200 # Node ID 3ea6c1cb3dab16e70cb463c7937516c2159ec75d # Parent 8f2ba236918b8883ae9326e03ba20a453082767a generalized type of lemma geometric_sum diff -r 8f2ba236918b -r 3ea6c1cb3dab src/HOL/SetInterval.thy --- a/src/HOL/SetInterval.thy Sun Apr 15 23:25:55 2007 +0200 +++ b/src/HOL/SetInterval.thy Mon Apr 16 04:02:15 2007 +0200 @@ -738,10 +738,11 @@ lemma geometric_sum: "x ~= 1 ==> (\<Sum>i=0..<n. x ^ i) = - (x ^ n - 1) / (x - 1::'a::{field, recpower, division_by_zero})" + (x ^ n - 1) / (x - 1::'a::{field, recpower})" apply (induct "n", auto) apply (rule_tac c = "x - 1" in field_mult_cancel_right_lemma) apply (auto simp add: mult_assoc left_distrib) + apply (simp add: times_divide_eq_right [symmetric] divide_self) apply (simp add: right_distrib diff_minus mult_commute power_Suc) done