diff options
| -rw-r--r-- | CHANGELOG_UNRELEASED.md | 4 | ||||
| -rw-r--r-- | mathcomp/ssreflect/ssrnat.v | 14 |
2 files changed, 13 insertions, 5 deletions
diff --git a/CHANGELOG_UNRELEASED.md b/CHANGELOG_UNRELEASED.md index 9a14eec..69f53ea 100644 --- a/CHANGELOG_UNRELEASED.md +++ b/CHANGELOG_UNRELEASED.md @@ -37,7 +37,7 @@ The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/). - Arithmetic theorems in ssrnat and div: - some trivial results in ssrnat: `ltn_predl`, `ltn_predr`, - `ltn_subr` and `predn_sub`, + `ltn_subr`, `leq_subl`, `ltn_subl` and `predn_sub`, - theorems about `n <=/< p +/- m` and `m +/- n <=/< p`: `leq_psubRL`, `ltn_psubLR`, `leq_subRL`, `ltn_subLR`, `leq_subCl`, `leq_psubCr`, `leq_subCr`, `ltn_subCr`, `ltn_psubCl` and @@ -119,6 +119,8 @@ The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/). `ssrnat.mc_1_9` module. One may compile proofs compatible with the version 1.9 in newer versions by using this module. +- `leq_subr` has been renamed `leq_subl` (and the latter has been reallocated) + ### Removed - `fin_inj_bij` lemma is removed as a duplicate of `injF_bij` lemma diff --git a/mathcomp/ssreflect/ssrnat.v b/mathcomp/ssreflect/ssrnat.v index f358f7b..434479d 100644 --- a/mathcomp/ssreflect/ssrnat.v +++ b/mathcomp/ssreflect/ssrnat.v @@ -326,7 +326,7 @@ Hint Resolve leqnSn : core. Lemma leq_pred n : n.-1 <= n. Proof. by case: n => /=. Qed. Lemma leqSpred n : n <= n.-1.+1. Proof. by case: n => /=. Qed. -Lemma ltn_predl n : (n.-1 < n) = (n != 0). +Lemma ltn_predl n : (n.-1 < n) = (0 < n). Proof. by case: n => [//|n]; rewrite ltnSn. Qed. Lemma ltn_predr m n : (m < n.-1) = (m.+1 < n). @@ -517,6 +517,15 @@ Proof. by rewrite -subn_eq0 -subnDA. Qed. Lemma leq_subr m n : n - m <= n. Proof. by rewrite leq_subLR leq_addl. Qed. +Lemma ltn_subl m n : n < n - m = false. +Proof. by rewrite ltnNge leq_subr. Qed. + +Lemma leq_subl m n : n <= n - m = (m == 0) || (n == 0). +Proof. by case: m n => [|m] [|n]; rewrite ?subn0 ?leqnn ?ltn_subl. Qed. + +Lemma ltn_subr m n : n - m < n = (0 < m) && (0 < n). +Proof. by rewrite ltnNge leq_subl negb_or !lt0n. Qed. + Lemma subnKC m n : m <= n -> m + (n - m) = n. Proof. by elim: m n => [|m IHm] [|n] // /(IHm n) {2}<-. Qed. @@ -538,9 +547,6 @@ Proof. by move=> le_pm le_pn; rewrite addnBA // addnBAC. Qed. Lemma subnBA m n p : p <= n -> m - (n - p) = m + p - n. Proof. by move=> le_pn; rewrite -{2}(subnK le_pn) subnDr. Qed. -Lemma ltn_subr m n : m <= n -> (n - m < n) = (m > 0). -Proof. by move=> le_mn; rewrite -subn_gt0 subnBA// addKn. Qed. - Lemma subKn m n : m <= n -> n - (n - m) = m. Proof. by move/subnBA->; rewrite addKn. Qed. |