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| author |  Stephane Glondu <steph@glondu.net> | 2012-01-12 16:02:20 +0100 |
|---|---|---|
| committer | Stephane Glondu <steph@glondu.net> | 2012-01-12 16:02:20 +0100 |
| commit | 97fefe1fcca363a1317e066e7f4b99b9c1e9987b (patch) | |
| tree | 97ec6b7d831cc5fb66328b0c63a11db1cbb2f158 /plugins/omega/OmegaLemmas.v | |
| parent | 300293c119981054c95182a90c829058530a6b6f (diff) | |
Imported Upstream version 8.4~betaupstream/8.4_beta
Diffstat (limited to 'plugins/omega/OmegaLemmas.v')
| -rw-r--r-- | plugins/omega/OmegaLemmas.v | 9 |
1 files changed, 7 insertions, 2 deletions
diff --git a/plugins/omega/OmegaLemmas.v b/plugins/omega/OmegaLemmas.v index ec9faedd..5b6f4670 100644 --- a/plugins/omega/OmegaLemmas.v +++ b/plugins/omega/OmegaLemmas.v @@ -6,8 +6,6 @@ (* * GNU Lesser General Public License Version 2.1 *) (***********************************************************************) -(*i $Id: OmegaLemmas.v 12337 2009-09-17 15:58:14Z glondu $ i*) - Require Import ZArith_base. Open Local Scope Z_scope. @@ -300,3 +298,10 @@ Definition fast_Zred_factor5 (x y : Z) (P : Z -> Prop) Definition fast_Zred_factor6 (x : Z) (P : Z -> Prop) (H : P (x + 0)) := eq_ind_r P H (Zred_factor6 x). + +Theorem intro_Z : + forall n:nat, exists y : Z, Z_of_nat n = y /\ 0 <= y * 1 + 0. +Proof. + intros n; exists (Z_of_nat n); split; trivial. + rewrite Zmult_1_r, Zplus_0_r. apply Zle_0_nat. +Qed. |