diff options
Diffstat (limited to 'theories/Numbers/Cyclic/DoubleCyclic/DoubleLift.v')
| -rw-r--r-- | theories/Numbers/Cyclic/DoubleCyclic/DoubleLift.v | 34 |
1 files changed, 12 insertions, 22 deletions
diff --git a/theories/Numbers/Cyclic/DoubleCyclic/DoubleLift.v b/theories/Numbers/Cyclic/DoubleCyclic/DoubleLift.v index 21e694e57..3405b6f4d 100644 --- a/theories/Numbers/Cyclic/DoubleCyclic/DoubleLift.v +++ b/theories/Numbers/Cyclic/DoubleCyclic/DoubleLift.v @@ -106,17 +106,9 @@ Section DoubleLift. Variable spec_w_W0 : forall h, [[w_W0 h]] = [|h|] * wB. Variable spec_w_0W : forall l, [[w_0W l]] = [|l|]. Variable spec_compare : forall x y, - match w_compare x y with - | Eq => [|x|] = [|y|] - | Lt => [|x|] < [|y|] - | Gt => [|x|] > [|y|] - end. + w_compare x y = Zcompare [|x|] [|y|]. Variable spec_ww_compare : forall x y, - match ww_compare x y with - | Eq => [[x]] = [[y]] - | Lt => [[x]] < [[y]] - | Gt => [[x]] > [[y]] - end. + ww_compare x y = Zcompare [[x]] [[y]]. Variable spec_ww_digits : ww_Digits = xO w_digits. Variable spec_w_head00 : forall x, [|x|] = 0 -> [|w_head0 x|] = Zpos w_digits. Variable spec_w_head0 : forall x, 0 < [|x|] -> @@ -159,7 +151,7 @@ Section DoubleLift. absurd (0 < [|xh|] * wB + [|xl|]); auto with zarith. rewrite <- Hy3; rewrite Zplus_0_r; auto with zarith. apply Zmult_lt_0_compat; auto with zarith. - generalize (spec_compare w_0 xh); case w_compare. + rewrite spec_compare. case Zcompare_spec. intros H; simpl. rewrite spec_w_add; rewrite spec_w_head00. rewrite spec_zdigits; rewrite spec_ww_digits. @@ -176,9 +168,8 @@ Section DoubleLift. rewrite wwB_div_2;rewrite Zmult_comm;rewrite wwB_wBwB. assert (U:= lt_0_wB w_digits); destruct x as [ |xh xl];simpl ww_to_Z;intros H. unfold Zlt in H;discriminate H. - assert (H0 := spec_compare w_0 xh);rewrite spec_w_0 in H0. - destruct (w_compare w_0 xh). - rewrite <- H0. simpl Zplus. rewrite <- H0 in H;simpl in H. + rewrite spec_compare, spec_w_0. case Zcompare_spec; intros H0. + rewrite <- H0 in *. simpl Zplus. simpl in H. case (spec_to_Z w_zdigits); case (spec_to_Z (w_head0 xl)); intros HH1 HH2 HH3 HH4. rewrite spec_w_add. @@ -233,7 +224,7 @@ Section DoubleLift. apply Zmult_lt_0_compat; auto with zarith. assert (F2: [|xl|] = 0). rewrite F1 in Hx; auto with zarith. - generalize (spec_compare w_0 xl); case w_compare. + rewrite spec_compare; case Zcompare_spec. intros H; simpl. rewrite spec_w_add; rewrite spec_w_tail00; auto. rewrite spec_zdigits; rewrite spec_ww_digits. @@ -248,8 +239,7 @@ Section DoubleLift. clear spec_ww_zdigits. destruct x as [ |xh xl];simpl ww_to_Z;intros H. unfold Zlt in H;discriminate H. - assert (H0 := spec_compare w_0 xl);rewrite spec_w_0 in H0. - destruct (w_compare w_0 xl). + rewrite spec_compare, spec_w_0. case Zcompare_spec; intros H0. rewrite <- H0; rewrite Zplus_0_r. case (spec_to_Z (w_tail0 xh)); intros HH1 HH2. generalize H; rewrite <- H0; rewrite Zplus_0_r; clear H; intros H. @@ -323,7 +313,7 @@ Section DoubleLift. assert (Hx := spec_ww_to_Z w_digits w_to_Z spec_to_Z (WW xh xl)); simpl in Hx;assert (Hyh := spec_to_Z yh);assert (Hyl:=spec_to_Z yl); assert (Hy:=spec_ww_to_Z w_digits w_to_Z spec_to_Z (WW yh yl));simpl in Hy. - generalize (spec_ww_compare p zdigits); case ww_compare; intros H1. + rewrite spec_ww_compare; case Zcompare_spec; intros H1. rewrite H1; unfold zdigits; rewrite spec_w_0W. rewrite spec_zdigits; rewrite Zminus_diag; rewrite Zplus_0_r. simpl ww_to_Z; w_rewrite;zarith. @@ -365,7 +355,7 @@ Section DoubleLift. ring_simplify ([[p]] + (Zpos w_digits - [[p]]));fold wB;zarith. assert (Hv: [[p]] > Zpos w_digits). generalize H1; clear H1. - unfold zdigits; rewrite spec_w_0W; rewrite spec_zdigits; auto. + unfold zdigits; rewrite spec_w_0W; rewrite spec_zdigits; auto with zarith. clear H1. assert (HH0: [|low (ww_sub p zdigits)|] = [[p]] - Zpos w_digits). rewrite spec_low. @@ -446,8 +436,7 @@ Section DoubleLift. clear H1;w_rewrite);simpl ww_add_mul_div. replace [[WW w_0 w_0]] with 0;[w_rewrite|simpl;w_rewrite;trivial]. intros Heq;rewrite <- Heq;clear Heq; auto. - generalize (spec_ww_compare p (w_0W w_zdigits)); - case ww_compare; intros H1; w_rewrite. + rewrite spec_ww_compare. case Zcompare_spec; intros H1; w_rewrite. rewrite (spec_w_add_mul_div w_0 w_0);w_rewrite;zarith. generalize H1; w_rewrite; rewrite spec_zdigits; clear H1; intros H1. assert (HH0: [|low p|] = [[p]]). @@ -464,7 +453,8 @@ Section DoubleLift. rewrite (spec_w_add_mul_div w_0 w_0);w_rewrite;zarith. rewrite Zpos_xO in H;zarith. assert (HH: [|low (ww_sub p (w_0W w_zdigits)) |] = [[p]] - Zpos w_digits). - generalize H1; clear H1. + symmetry in H1; change ([[p]] > [[w_0W w_zdigits]]) in H1. + revert H1. rewrite spec_low. rewrite spec_ww_sub; w_rewrite; intros H1. rewrite <- Zmod_div_mod; auto with zarith. |