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| author |  herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2009-10-04 10:05:11 +0000 |
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| committer | herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2009-10-04 10:05:11 +0000 |
| commit | 4b993912cc6c6135e41ea959f934fa73d1da05ab (patch) | |
| tree | b187153d7aa33166fe3886aca46031ac16b1879c /theories/ZArith/Zmin.v | |
| parent | a40e92559339d41eb3a757968de4367d77df712f (diff) | |
Some new lemmas on max and min and a fix for a wrongly stated lemma in r12358.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12370 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/ZArith/Zmin.v')
| -rw-r--r-- | theories/ZArith/Zmin.v | 12 |
1 files changed, 12 insertions, 0 deletions
diff --git a/theories/ZArith/Zmin.v b/theories/ZArith/Zmin.v index dd35cd139..de83af137 100644 --- a/theories/ZArith/Zmin.v +++ b/theories/ZArith/Zmin.v @@ -80,6 +80,18 @@ Proof. intros; apply Zmin_case; assumption. Qed. +(** * Compatibility with order *) + +Lemma Zle_min_compat_r : forall n m p, n <= m -> Zmin n p <= Zmin m p. +Proof. + intros; do 2 (apply Zmin_case_strong; intro); eauto using Zle_trans, Zle_refl. +Qed. + +Lemma Zle_min_compat_l : forall n m p, n <= m -> Zmin p n <= Zmin p m. +Proof. + intros; do 2 (apply Zmin_case_strong; intro); eauto using Zle_trans, Zle_refl. +Qed. + (** * Semi-lattice properties of min *) Lemma Zmin_idempotent : forall n:Z, Zmin n n = n. |