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Diffstat (limited to 'theories/Numbers/Integer/Abstract/ZDivTrunc.v')
| -rw-r--r-- | theories/Numbers/Integer/Abstract/ZDivTrunc.v | 8 |
1 files changed, 8 insertions, 0 deletions
diff --git a/theories/Numbers/Integer/Abstract/ZDivTrunc.v b/theories/Numbers/Integer/Abstract/ZDivTrunc.v index 46c36015d..bbb8ad5ae 100644 --- a/theories/Numbers/Integer/Abstract/ZDivTrunc.v +++ b/theories/Numbers/Integer/Abstract/ZDivTrunc.v @@ -622,6 +622,14 @@ Proof. apply quot_rem; order. Qed. +Lemma rem_quot: forall a b, b~=0 -> + a rem b รท b == 0. +Proof. + intros a b Hb. + rewrite quot_small_iff by assumption. + auto using rem_bound_abs. +Qed. + (** A last inequality: *) Theorem quot_mul_le: |