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Replace the use of omega with lia #38

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May 13, 2021
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Replace the use of omega with lia #38

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1 change: 1 addition & 0 deletions .github/workflows/docker-action.yml
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Expand Up @@ -17,6 +17,7 @@ jobs:
strategy:
matrix:
image:
- 'mathcomp/mathcomp:1.12.0-coq-dev'
- 'mathcomp/mathcomp:1.12.0-coq-8.13'
- 'mathcomp/mathcomp:1.12.0-coq-8.12'
- 'mathcomp/mathcomp:1.12.0-coq-8.11'
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2 changes: 2 additions & 0 deletions meta.yml
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Expand Up @@ -83,6 +83,8 @@ dependencies:
[MathComp](https://math-comp.github.io) 1.11.0 or later

tested_coq_opam_versions:
- version: '1.12.0-coq-dev'
repo: 'mathcomp/mathcomp'
- version: '1.12.0-coq-8.13'
repo: 'mathcomp/mathcomp'
- version: '1.12.0-coq-8.12'
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6 changes: 3 additions & 3 deletions refinements/binnat.v
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@@ -1,6 +1,6 @@
(** This file is part of CoqEAL, the Coq Effective Algebra Library.
(c) Copyright INRIA and University of Gothenburg, see LICENSE *)
Require Import ZArith.
Require Import ZArith Lia.

From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat div seq zmodp.
From mathcomp Require Import path choice fintype tuple finset ssralg ssrnum bigop ssrint.
Expand Down Expand Up @@ -405,13 +405,13 @@ Qed.
Lemma Nat2Pos_xI m : ((Pos.of_nat m.+1)~1)%positive = Pos.of_nat ((m.+1).*2.+1).
Proof.
rewrite -muln2 [RHS]Nat2Pos.inj_succ // Nat2Pos.inj_mul //.
simpl (Pos.of_nat 2); zify; omega.
simpl (Pos.of_nat 2); lia.
Qed.

Lemma Nat2Pos_xO m : ((Pos.of_nat m.+1)~0)%positive = Pos.of_nat ((m.+1).*2).
Proof.
rewrite -muln2 Nat2Pos.inj_mul //.
simpl (Pos.of_nat 2); zify; omega.
simpl (Pos.of_nat 2); lia.
Qed.

Lemma pos_of_natE m n : pos_of_nat m n = Pos.of_nat (maxn 1 (m.*2.+1 - n)).
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4 changes: 2 additions & 2 deletions refinements/binrat.v
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@@ -1,6 +1,6 @@
(** * A refinement of Mathcomp's rationals [rat] with [bigQ] from Coq standard library. *)

Require Import ZArith QArith.
Require Import ZArith QArith Lia.
From Bignums Require Import BigQ.
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat order.
From mathcomp Require Import ssralg ssrnum ssrint rat div.
Expand Down Expand Up @@ -215,7 +215,7 @@ Qed.

Lemma Z2int_lt x y : (Z2int x < Z2int y)%R <-> Z.lt x y.
Proof.
rewrite -lez_addr1 -[1%R]/(Z2int 1) -Z2int_add Z2int_le; omega.
rewrite -lez_addr1 -[1%R]/(Z2int 1) -Z2int_add Z2int_le; lia.
Qed.

Lemma nat_of_pos_Z_to_pos x : nat_of_pos x = `|Z2int (Z.pos x)|%N.
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