diff options
Diffstat (limited to 'theories/ZArith/Zpower.v')
| -rw-r--r-- | theories/ZArith/Zpower.v | 14 |
1 files changed, 7 insertions, 7 deletions
diff --git a/theories/ZArith/Zpower.v b/theories/ZArith/Zpower.v index 5052d01a..0d9b08d6 100644 --- a/theories/ZArith/Zpower.v +++ b/theories/ZArith/Zpower.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 *) @@ -78,7 +78,7 @@ Proof. Qed. Hint Immediate Zpower_nat_is_exp Zpower_pos_is_exp : zarith. -Hint Unfold Zpower_pos Zpower_nat: zarith. +Hint Unfold Z.pow_pos Zpower_nat: zarith. Theorem Zpower_exp x n m : n >= 0 -> m >= 0 -> x ^ (n + m) = x ^ n * x ^ m. @@ -181,7 +181,7 @@ Section Powers_of_2. Qed. Theorem shift_pos_correct p x : - Zpos (shift_pos p x) = Zpower_pos 2 p * Zpos x. + Zpos (shift_pos p x) = Z.pow_pos 2 p * Zpos x. Proof. now rewrite shift_pos_nat, Zpower_pos_nat, shift_nat_correct. Qed. @@ -266,13 +266,13 @@ Section power_div_with_rest. apply Pos.iter_invariant; [|omega]. intros ((q,r),d) (H,H'). unfold Zdiv_rest_aux. destruct q as [ |[q|q| ]|[q|q| ]]; try omega. - - rewrite Z.pos_xI, Z.mul_add_distr_r in H. + - rewrite Pos2Z.inj_xI, Z.mul_add_distr_r in H. rewrite Z.mul_shuffle3, Z.mul_assoc. omega. - - rewrite Z.pos_xO in H. + - rewrite Pos2Z.inj_xO in H. rewrite Z.mul_shuffle3, Z.mul_assoc. omega. - - rewrite Z.neg_xI, Z.mul_sub_distr_r in H. + - rewrite Pos2Z.neg_xI, Z.mul_sub_distr_r in H. rewrite Z.mul_sub_distr_r, Z.mul_shuffle3, Z.mul_assoc. omega. - - rewrite Z.neg_xO in H. + - rewrite Pos2Z.neg_xO in H. rewrite Z.mul_shuffle3, Z.mul_assoc. omega. Qed. |