diff options
Diffstat (limited to 'theories/Numbers/Cyclic/DoubleCyclic/DoubleSqrt.v')
| -rw-r--r-- | theories/Numbers/Cyclic/DoubleCyclic/DoubleSqrt.v | 20 |
1 files changed, 10 insertions, 10 deletions
diff --git a/theories/Numbers/Cyclic/DoubleCyclic/DoubleSqrt.v b/theories/Numbers/Cyclic/DoubleCyclic/DoubleSqrt.v index 149682f8..ab8c8617 100644 --- a/theories/Numbers/Cyclic/DoubleCyclic/DoubleSqrt.v +++ b/theories/Numbers/Cyclic/DoubleCyclic/DoubleSqrt.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 *) @@ -185,17 +185,17 @@ Section DoubleSqrt. 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). @@ -266,8 +266,8 @@ Section DoubleSqrt. if ww_is_even x then [[x]] mod 2 = 0 else [[x]] mod 2 = 1. clear spec_more_than_1_digit. intros x; case x; simpl ww_is_even. + reflexivity. simpl. - rewrite Zmod_small; auto with zarith. intros w1 w2; simpl. unfold base. rewrite Zplus_mod; auto with zarith. @@ -692,7 +692,7 @@ intros x; case x; simpl ww_is_even. intros x y H; unfold ww_sqrt2. repeat match goal with |- context[split ?x] => generalize (spec_split x); case (split x) - end; simpl fst; simpl snd. + end; simpl @fst; simpl @snd. intros w0 w1 Hw0 w2 w3 Hw1. assert (U: wB/4 <= [|w2|]). case (Z.le_gt_cases (wB / 4) [|w2|]); auto; intros H1. @@ -761,7 +761,7 @@ intros x; case x; simpl ww_is_even. auto. split. unfold zn2z_to_Z; rewrite <- Hw1. - unfold ww_to_Z, zn2z_to_Z in H1; rewrite H1. + unfold ww_to_Z, zn2z_to_Z in H1. rewrite H1. rewrite <- Hw0. match goal with |- (?X ^2 + ?Y) * wwB + (?Z * wB + ?T) = ?U => transitivity ((X * wB) ^ 2 + (Y * wB + Z) * wB + T) @@ -1193,7 +1193,7 @@ Qed. rewrite <- wwB_4_wB_4; auto. generalize (@spec_w_sqrt2 w0 w1 V);auto with zarith. case (w_sqrt2 w0 w1); intros w2 c. - simpl ww_to_Z; simpl fst. + simpl ww_to_Z; simpl @fst. case c; unfold interp_carry; autorewrite with rm10. intros w3 (H6, H7); rewrite H6. assert (V1 := spec_to_Z w3);auto with zarith. @@ -1256,7 +1256,7 @@ Qed. generalize (@spec_w_sqrt2 w0 w1 V);auto with zarith. case (w_sqrt2 w0 w1); intros w2 c. case (spec_to_Z w2); intros HH1 HH2. - simpl ww_to_Z; simpl fst. + simpl ww_to_Z; simpl @fst. assert (Hv3: [[ww_pred ww_zdigits]] = Zpos (xO w_digits) - 1). rewrite spec_ww_pred; rewrite spec_ww_zdigits. |