diff options
Diffstat (limited to 'plugins/btauto/Algebra.v')
| -rw-r--r-- | plugins/btauto/Algebra.v | 24 |
1 files changed, 12 insertions, 12 deletions
diff --git a/plugins/btauto/Algebra.v b/plugins/btauto/Algebra.v index ee7341a4..f1095fc9 100644 --- a/plugins/btauto/Algebra.v +++ b/plugins/btauto/Algebra.v @@ -1,4 +1,4 @@ -Require Import Bool PArith DecidableClass Omega ROmega. +Require Import Bool PArith DecidableClass Omega Lia. Ltac bool := repeat match goal with @@ -84,9 +84,9 @@ Ltac case_decide := match goal with let H := fresh "H" in define (@decide P D) b H; destruct b; try_decide | [ |- context [Pos.compare ?x ?y] ] => - destruct (Pos.compare_spec x y); try (exfalso; zify; romega) + destruct (Pos.compare_spec x y); try lia | [ X : context [Pos.compare ?x ?y] |- _ ] => - destruct (Pos.compare_spec x y); try (exfalso; zify; romega) + destruct (Pos.compare_spec x y); try lia end. Section Definitions. @@ -325,13 +325,13 @@ Qed. Lemma linear_le_compat : forall k l p, linear k p -> (k <= l)%positive -> linear l p. Proof. -intros k l p H; revert l; induction H; constructor; eauto; zify; romega. +intros k l p H; revert l; induction H; constructor; eauto; lia. Qed. Lemma linear_valid_incl : forall k p, linear k p -> valid k p. Proof. intros k p H; induction H; constructor; auto. -eapply valid_le_compat; eauto; zify; romega. +eapply valid_le_compat; eauto; lia. Qed. End Validity. @@ -417,13 +417,13 @@ Qed. Hint Extern 5 => match goal with | [ |- (Pos.max ?x ?y <= ?z)%positive ] => - apply Pos.max_case_strong; intros; zify; romega + apply Pos.max_case_strong; intros; lia | [ |- (?z <= Pos.max ?x ?y)%positive ] => - apply Pos.max_case_strong; intros; zify; romega + apply Pos.max_case_strong; intros; lia | [ |- (Pos.max ?x ?y < ?z)%positive ] => - apply Pos.max_case_strong; intros; zify; romega + apply Pos.max_case_strong; intros; lia | [ |- (?z < Pos.max ?x ?y)%positive ] => - apply Pos.max_case_strong; intros; zify; romega + apply Pos.max_case_strong; intros; lia | _ => zify; omega end. Hint Resolve Pos.le_max_r Pos.le_max_l. @@ -445,8 +445,8 @@ intros kl kr pl pr Hl Hr; revert kr pr Hr; induction Hl; intros kr pr Hr; simpl. now rewrite <- (Pos.max_id i); intuition. destruct (Pos.compare_spec i i0); subst; try case_decide; repeat (constructor; intuition). + apply (valid_le_compat (Pos.max i0 i0)); [now auto|]; rewrite Pos.max_id; auto. - + apply (valid_le_compat (Pos.max i0 i0)); [now auto|]; rewrite Pos.max_id; zify; romega. - + apply (valid_le_compat (Pos.max (Pos.succ i0) (Pos.succ i0))); [now auto|]; rewrite Pos.max_id; zify; romega. + + apply (valid_le_compat (Pos.max i0 i0)); [now auto|]; rewrite Pos.max_id; lia. + + apply (valid_le_compat (Pos.max (Pos.succ i0) (Pos.succ i0))); [now auto|]; rewrite Pos.max_id; lia. + apply (valid_le_compat (Pos.max (Pos.succ i) i0)); intuition. + apply (valid_le_compat (Pos.max i (Pos.succ i0))); intuition. } @@ -456,7 +456,7 @@ Lemma poly_mul_cst_valid_compat : forall k v p, valid k p -> valid k (poly_mul_c Proof. intros k v p H; induction H; simpl; [now auto|]. case_decide; [|now auto]. -eapply (valid_le_compat i); [now auto|zify; romega]. +eapply (valid_le_compat i); [now auto|lia]. Qed. Lemma poly_mul_mon_null_compat : forall i p, null (poly_mul_mon i p) -> null p. |