diff options
Diffstat (limited to 'theories/Numbers/Cyclic/DoubleCyclic/DoubleMul.v')
| -rw-r--r-- | theories/Numbers/Cyclic/DoubleCyclic/DoubleMul.v | 12 |
1 files changed, 6 insertions, 6 deletions
diff --git a/theories/Numbers/Cyclic/DoubleCyclic/DoubleMul.v b/theories/Numbers/Cyclic/DoubleCyclic/DoubleMul.v index 1c0fc68a..537f557d 100644 --- a/theories/Numbers/Cyclic/DoubleCyclic/DoubleMul.v +++ b/theories/Numbers/Cyclic/DoubleCyclic/DoubleMul.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2014 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) @@ -218,17 +218,17 @@ Section DoubleMul. Notation wwB := (base (ww_digits w_digits)). Notation "[| x |]" := (w_to_Z x) (at level 0, x at level 99). Notation "[+| c |]" := - (interp_carry 1 wB w_to_Z c) (at level 0, x at level 99). + (interp_carry 1 wB w_to_Z c) (at level 0, c at level 99). Notation "[-| c |]" := - (interp_carry (-1) wB w_to_Z c) (at level 0, x at level 99). + (interp_carry (-1) wB w_to_Z c) (at level 0, c at level 99). Notation "[[ x ]]" := (ww_to_Z w_digits w_to_Z x)(at level 0, x at level 99). Notation "[+[ c ]]" := (interp_carry 1 wwB (ww_to_Z w_digits w_to_Z) c) - (at level 0, x at level 99). + (at level 0, c at level 99). Notation "[-[ c ]]" := (interp_carry (-1) wwB (ww_to_Z w_digits w_to_Z) c) - (at level 0, x at level 99). + (at level 0, c at level 99). Notation "[|| x ||]" := (zn2z_to_Z wwB (ww_to_Z w_digits w_to_Z) x) (at level 0, x at level 99). @@ -328,7 +328,7 @@ Section DoubleMul. rewrite <- (Z.add_0_r ([|wc|]*wB));rewrite H;apply mult_add_ineq3;zarith. simpl ww_to_Z in H1. assert (U:=spec_to_Z cch). assert ([|wc|]*wB + [|cch|] <= 2*wB - 3). - destruct (Z_le_gt_dec ([|wc|]*wB + [|cch|]) (2*wB - 3));trivial. + destruct (Z_le_gt_dec ([|wc|]*wB + [|cch|]) (2*wB - 3)) as [Hle|Hgt];trivial. assert ([|xh|] * [|yl|] + [|xl|] * [|yh|] <= (2*wB - 4)*wB + 2). ring_simplify ((2*wB - 4)*wB + 2). assert (H4 := Zmult_lt_b _ _ _ (spec_to_Z xh) (spec_to_Z yl)). |