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Diffstat (limited to 'theories/ZArith/Zdiv_def.v')
| -rw-r--r-- | theories/ZArith/Zdiv_def.v | 37 |
1 files changed, 0 insertions, 37 deletions
diff --git a/theories/ZArith/Zdiv_def.v b/theories/ZArith/Zdiv_def.v deleted file mode 100644 index 0f375e1448..0000000000 --- a/theories/ZArith/Zdiv_def.v +++ /dev/null @@ -1,37 +0,0 @@ -(************************************************************************) -(* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *) -(* \VV/ **************************************************************) -(* // * This file is distributed under the terms of the *) -(* * GNU Lesser General Public License Version 2.1 *) -(************************************************************************) - -Require Import BinPos BinNat BinInt Zbool Zcompare Zorder Zabs Znat. -Local Open Scope Z_scope. - -Notation Zdiv_eucl_POS := Z.pos_div_eucl (only parsing). -Notation Zdiv_eucl := Z.div_eucl (only parsing). -Notation Zdiv := Z.div (only parsing). -Notation Zmod := Z.modulo (only parsing). -Notation Zquotrem := Z.quotrem (only parsing). -Notation Zquot := Z.quot (only parsing). -Notation Zrem := Z.rem (only parsing). - -Lemma Zdiv_eucl_POS_eq : forall a b, 0 < b -> - let (q, r) := Zdiv_eucl_POS a b in Zpos a = b * q + r. -Proof. - intros a b Hb. generalize (Z.pos_div_eucl_eq a b Hb). - destruct Z.pos_div_eucl. now rewrite Z.mul_comm. -Qed. - -Notation Zdiv_eucl_eq := Z.div_eucl_eq (only parsing). -Notation Z_div_mod_eq_full := Z.div_mod (only parsing). -Notation Zmod_POS_bound := Z.pos_div_eucl_bound (only parsing). -Notation Zmod_pos_bound := Z.mod_pos_bound (only parsing). -Notation Zmod_neg_bound := Z.mod_neg_bound (only parsing). - -Notation Zquotrem_eq := Z.quotrem_eq (only parsing). -Notation Z_quot_rem_eq := Z.quot_rem' (only parsing). -Notation Zrem_bound := Z.rem_bound_pos (only parsing). -Notation Zrem_opp_l := Z.rem_opp_l' (only parsing). -Notation Zrem_opp_r := Z.rem_opp_r' (only parsing). |