diff options
Diffstat (limited to 'theories/Numbers/Integer/Abstract/ZDivTrunc.v')
| -rw-r--r-- | theories/Numbers/Integer/Abstract/ZDivTrunc.v | 18 |
1 files changed, 14 insertions, 4 deletions
diff --git a/theories/Numbers/Integer/Abstract/ZDivTrunc.v b/theories/Numbers/Integer/Abstract/ZDivTrunc.v index 04301077..31e42738 100644 --- a/theories/Numbers/Integer/Abstract/ZDivTrunc.v +++ b/theories/Numbers/Integer/Abstract/ZDivTrunc.v @@ -1,9 +1,11 @@ (************************************************************************) -(* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) +(* * The Coq Proof Assistant / The Coq Development Team *) +(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *) +(* <O___,, * (see CREDITS file for the list of authors) *) (* \VV/ **************************************************************) -(* // * This file is distributed under the terms of the *) -(* * GNU Lesser General Public License Version 2.1 *) +(* // * This file is distributed under the terms of the *) +(* * GNU Lesser General Public License Version 2.1 *) +(* * (see LICENSE file for the text of the license) *) (************************************************************************) Require Import ZAxioms ZMulOrder ZSgnAbs NZDiv. @@ -622,6 +624,14 @@ 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: |