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| author |  letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2010-11-02 15:10:47 +0000 |
|---|---|---|
| committer | letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2010-11-02 15:10:47 +0000 |
| commit | 0cb098205ba6d85674659bf5d0bfc0ed942464cc (patch) | |
| tree | 47a7cb0e585ecafe0fe18d6f8061cf513ead3dc4 /theories/ZArith/Zorder.v | |
| parent | d6ebd62341fd6bbe2b7d4e5309d8e13f786a9462 (diff) | |
Numbers: misc improvements
- Add alternate specifications of pow and sqrt
- Slightly more general pow_lt_mono_r
- More explicit equivalence of Plog2_Z and log_inf
- Nicer proofs in Zpower
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13607 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/ZArith/Zorder.v')
| -rw-r--r-- | theories/ZArith/Zorder.v | 8 |
1 files changed, 8 insertions, 0 deletions
diff --git a/theories/ZArith/Zorder.v b/theories/ZArith/Zorder.v index ebce8ccdc..1bd833d6f 100644 --- a/theories/ZArith/Zorder.v +++ b/theories/ZArith/Zorder.v @@ -449,6 +449,14 @@ Proof. split; [apply Zlt_succ_le | apply Zle_lt_succ]. Qed. +Lemma Zle_succ_l : forall n m, Zsucc n <= m <-> n < m. +Proof. + intros. split; intros H. + rewrite (Zsucc_pred m). apply Zle_lt_succ, Zsucc_le_reg. + now rewrite <- Zsucc_pred. + now apply Zlt_le_succ. +Qed. + (** Weakening order *) Lemma Zle_succ : forall n:Z, n <= Zsucc n. |