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Diffstat (limited to 'theories/Numbers/Integer/Abstract/ZPow.v')
| -rw-r--r-- | theories/Numbers/Integer/Abstract/ZPow.v | 13 |
1 files changed, 12 insertions, 1 deletions
diff --git a/theories/Numbers/Integer/Abstract/ZPow.v b/theories/Numbers/Integer/Abstract/ZPow.v index 53d84dce..d30cea33 100644 --- a/theories/Numbers/Integer/Abstract/ZPow.v +++ b/theories/Numbers/Integer/Abstract/ZPow.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) @@ -18,6 +18,17 @@ Module Type ZPowProp Include NZPowProp A A B. +(** A particular case of [pow_add_r], with no precondition *) + +Lemma pow_twice_r a b : a^(2*b) == a^b * a^b. +Proof. + rewrite two_succ. nzsimpl. + destruct (le_gt_cases 0 b). + - now rewrite pow_add_r. + - rewrite !pow_neg_r. now nzsimpl. trivial. + now apply add_neg_neg. +Qed. + (** Parity of power *) Lemma even_pow : forall a b, 0<b -> even (a^b) = even a. |