diff options
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 *) |