# HG changeset patch # User obua # Date 1181229703 -7200 # Node ID 77577fc2f14108b272b25b5b8c6c28b65b276f4e # Parent 1c39f1bd1f5347d8dfe790ce2cfc45ca896d28b3 deleted comments diff -r 1c39f1bd1f53 -r 77577fc2f141 src/HOL/Real/RealPow.thy --- a/src/HOL/Real/RealPow.thy Thu Jun 07 14:26:05 2007 +0200 +++ b/src/HOL/Real/RealPow.thy Thu Jun 07 17:21:43 2007 +0200 @@ -28,32 +28,6 @@ qed -(*lemma realpow_zero_zero: "r ^ n = (0::real) ==> r = 0" -by simp - -lemma realpow_two: "(r::real)^ (Suc (Suc 0)) = r * r" -by simp - -text{*Legacy: weaker version of the theorem @{text power_strict_mono}*} -lemma realpow_less: - "[|(0::real) < x; x < y; 0 < n|] ==> x ^ n < y ^ n" -thm power_strict_mono -apply (rule power_strict_mono, auto) -done *) - -(* declare [simp del]: zero_le_power - -lemma realpow_two_le [simp]: "(0::real) \ r^ Suc (Suc 0)" -by (simp) - - -lemma abs_realpow_two [simp]: "abs((x::real)^Suc (Suc 0)) = x^Suc (Suc 0)" -by (simp) - -lemma realpow_two_abs [simp]: "abs(x::real)^Suc (Suc 0) = x^Suc (Suc 0)" -by (simp) - -*) lemma two_realpow_ge_one [simp]: "(1::real) \ 2 ^ n" by (rule power_increasing[of 0 n "2::real", simplified])