# HG changeset patch # User huffman # Date 1179127644 -7200 # Node ID e499ded5d0fcb23ffa1745f662c4bc16ffbd1be3 # Parent 114cf19066813a02c0960da866fcbe44a069692a remove redundant lemmas diff -r 114cf1906681 -r e499ded5d0fc src/HOL/Hyperreal/NthRoot.thy --- a/src/HOL/Hyperreal/NthRoot.thy Mon May 14 09:16:47 2007 +0200 +++ b/src/HOL/Hyperreal/NthRoot.thy Mon May 14 09:27:24 2007 +0200 @@ -474,14 +474,11 @@ subsection {* Square Root of Sum of Squares *} -lemma "(sqrt (x\ + y\))\ = x\ + y\" -by simp - lemma real_sqrt_mult_self_sum_ge_zero [simp]: "0 \ sqrt(x*x + y*y)" -by (rule real_sqrt_ge_zero [OF real_mult_self_sum_ge_zero]) +by (rule real_sqrt_ge_zero [OF real_mult_self_sum_ge_zero]) lemma real_sqrt_sum_squares_ge_zero [simp]: "0 \ sqrt (x\ + y\)" -by (auto intro!: real_sqrt_ge_zero) +by simp lemma real_sqrt_sum_squares_mult_ge_zero [simp]: "0 \ sqrt ((x\ + y\)*(xa\ + ya\))" @@ -497,12 +494,6 @@ lemma real_sqrt_sum_squares_ge2 [simp]: "y \ sqrt(x\ + y\)" by (rule power2_le_imp_le, simp_all) -lemma real_sqrt_sos_less_one_iff: "(sqrt (x\ + y\) < 1) = (x\ + y\ < 1)" -by (rule real_sqrt_lt_1_iff) - -lemma real_sqrt_sos_eq_one_iff: "(sqrt (x\ + y\) = 1) = (x\ + y\ = 1)" -by (rule real_sqrt_eq_1_iff) - lemma power2_sum: fixes x y :: "'a::{number_ring,recpower}" shows "(x + y)\ = x\ + y\ + 2 * x * y"