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| author | filliatr | 2002-04-19 08:12:51 +0000 |
|---|---|---|
| committer | filliatr | 2002-04-19 08:12:51 +0000 |
| commit | 86503800a77326db19412ea1c3e534f79dc5d6d1 (patch) | |
| tree | 20fc455e1bce8670012bc1104566ed2a78c0d1ed /theories | |
| parent | 3120e870dc31b2ec753c90ea2ddda2ad9ba44548 (diff) | |
un thm de plus dans Zdiv; un retour chariot apres un message de la tactique FourierR
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@2659 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories')
| -rw-r--r-- | theories/ZArith/Zdiv.v | 8 |
1 files changed, 8 insertions, 0 deletions
diff --git a/theories/ZArith/Zdiv.v b/theories/ZArith/Zdiv.v index d3aa637bbb..b7876f3402 100644 --- a/theories/ZArith/Zdiv.v +++ b/theories/ZArith/Zdiv.v @@ -181,6 +181,14 @@ Intros. Absurd `(NEG p)>0`; [ Generalize (NEG_lt_ZERO p); Omega | Omega ]. Qed. +Theorem Z_div_mod_eq : (a,b:Z)`b > 0` -> `a = b * (Zdiv a b) + (Zmod a b)`. +Proof. +Unfold Zdiv Zmod. +Intros a b Hb. +Generalize (Z_div_mod a b Hb). +Pattern (Zdiv_eucl a b). +Case (Zdiv_eucl); Tauto. +Save. (** Existence theorems *) |