diff options
Diffstat (limited to 'theories/QArith/Qround.v')
| -rw-r--r-- | theories/QArith/Qround.v | 13 |
1 files changed, 12 insertions, 1 deletions
diff --git a/theories/QArith/Qround.v b/theories/QArith/Qround.v index 58a7967ed..ce363a33b 100644 --- a/theories/QArith/Qround.v +++ b/theories/QArith/Qround.v @@ -136,4 +136,15 @@ intros x y H. apply Zle_antisym. auto with *. symmetry in H; auto with *. -Qed.
\ No newline at end of file +Qed. + +Lemma Zdiv_Qdiv (n m: Z): (n / m)%Z = Qfloor (n / m). +Proof. + unfold Qfloor. intros. simpl. + destruct m as [?|?|p]; simpl. + now rewrite Zdiv_0_r, Zmult_0_r. + now rewrite Zmult_1_r. + rewrite <- Zopp_eq_mult_neg_1. + rewrite <- (Zopp_involutive (Zpos p)). + now rewrite Zdiv_opp_opp. +Qed. |