diff options
Diffstat (limited to 'theories/Numbers/Cyclic/Int31/Cyclic31.v')
| -rw-r--r-- | theories/Numbers/Cyclic/Int31/Cyclic31.v | 20 |
1 files changed, 9 insertions, 11 deletions
diff --git a/theories/Numbers/Cyclic/Int31/Cyclic31.v b/theories/Numbers/Cyclic/Int31/Cyclic31.v index bd4f0279..4a1f24b9 100644 --- a/theories/Numbers/Cyclic/Int31/Cyclic31.v +++ b/theories/Numbers/Cyclic/Int31/Cyclic31.v @@ -21,9 +21,7 @@ Require Import Znumtheory. Require Import Zgcd_alt. Require Import Zpow_facts. Require Import CyclicAxioms. -Require Import ROmega. - -Declare ML Module "int31_syntax_plugin". +Require Import Lia. Local Open Scope nat_scope. Local Open Scope int31_scope. @@ -128,7 +126,7 @@ Section Basics. Lemma nshiftl_S_tail : forall n x, nshiftl x (S n) = nshiftl (shiftl x) n. - Proof. + Proof. intros n; elim n; simpl; intros; now f_equal. Qed. @@ -1239,7 +1237,7 @@ Section Int31_Specs. destruct (Z_lt_le_dec (X+Y) wB). contradict H1; auto using Zmod_small with zarith. rewrite <- (Z_mod_plus_full (X+Y) (-1) wB). - rewrite Zmod_small; romega. + rewrite Zmod_small; lia. generalize (Z.compare_eq ((X+Y) mod wB) (X+Y)); intros Heq. destruct Z.compare; intros; @@ -1263,7 +1261,7 @@ Section Int31_Specs. destruct (Z_lt_le_dec (X+Y+1) wB). contradict H1; auto using Zmod_small with zarith. rewrite <- (Z_mod_plus_full (X+Y+1) (-1) wB). - rewrite Zmod_small; romega. + rewrite Zmod_small; lia. generalize (Z.compare_eq ((X+Y+1) mod wB) (X+Y+1)); intros Heq. destruct Z.compare; intros; @@ -1301,8 +1299,8 @@ Section Int31_Specs. unfold interp_carry; rewrite phi_phi_inv, Z.compare_eq_iff; intros. destruct (Z_lt_le_dec (X-Y) 0). rewrite <- (Z_mod_plus_full (X-Y) 1 wB). - rewrite Zmod_small; romega. - contradict H1; apply Zmod_small; romega. + rewrite Zmod_small; lia. + contradict H1; apply Zmod_small; lia. generalize (Z.compare_eq ((X-Y) mod wB) (X-Y)); intros Heq. destruct Z.compare; intros; @@ -1320,8 +1318,8 @@ Section Int31_Specs. unfold interp_carry; rewrite phi_phi_inv, Z.compare_eq_iff; intros. destruct (Z_lt_le_dec (X-Y-1) 0). rewrite <- (Z_mod_plus_full (X-Y-1) 1 wB). - rewrite Zmod_small; romega. - contradict H1; apply Zmod_small; romega. + rewrite Zmod_small; lia. + contradict H1; apply Zmod_small; lia. generalize (Z.compare_eq ((X-Y-1) mod wB) (X-Y-1)); intros Heq. destruct Z.compare; intros; @@ -1358,7 +1356,7 @@ Section Int31_Specs. change [|1|] with 1; change [|0|] with 0. rewrite <- (Z_mod_plus_full (0-[|x|]) 1 wB). rewrite Zminus_mod_idemp_l. - rewrite Zmod_small; generalize (phi_bounded x); romega. + rewrite Zmod_small; generalize (phi_bounded x); lia. Qed. Lemma spec_pred_c : forall x, [-|sub31c x 1|] = [|x|] - 1. |