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Diffstat (limited to 'theories/Numbers/Integer/Abstract/ZDivFloor.v')
| -rw-r--r-- | theories/Numbers/Integer/Abstract/ZDivFloor.v | 8 |
1 files changed, 8 insertions, 0 deletions
diff --git a/theories/Numbers/Integer/Abstract/ZDivFloor.v b/theories/Numbers/Integer/Abstract/ZDivFloor.v index ca6197002..a9077127e 100644 --- a/theories/Numbers/Integer/Abstract/ZDivFloor.v +++ b/theories/Numbers/Integer/Abstract/ZDivFloor.v @@ -650,6 +650,14 @@ Proof. apply div_mod; order. Qed. +Lemma mod_div: forall a b, b~=0 -> + a mod b / b == 0. +Proof. + intros a b Hb. + rewrite div_small_iff by assumption. + auto using mod_bound_or. +Qed. + (** A last inequality: *) Theorem div_mul_le: |