diff options
Diffstat (limited to 'theories/NArith/Ndiv_def.v')
| -rw-r--r-- | theories/NArith/Ndiv_def.v | 31 |
1 files changed, 31 insertions, 0 deletions
diff --git a/theories/NArith/Ndiv_def.v b/theories/NArith/Ndiv_def.v new file mode 100644 index 00000000..559f01f1 --- /dev/null +++ b/theories/NArith/Ndiv_def.v @@ -0,0 +1,31 @@ +(************************************************************************) +(* 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 BinNat. +Local Open Scope N_scope. + +(** Obsolete file, see [BinNat] now, + only compatibility notations remain here. *) + +Definition Pdiv_eucl a b := N.pos_div_eucl a (Npos b). + +Definition Pdiv_eucl_correct a b : + let (q,r) := Pdiv_eucl a b in Npos a = q * Npos b + r + := N.pos_div_eucl_spec a (Npos b). + +Lemma Pdiv_eucl_remainder a b : + snd (Pdiv_eucl a b) < Npos b. +Proof. now apply (N.pos_div_eucl_remainder a (Npos b)). Qed. + +Notation Ndiv_eucl := N.div_eucl (only parsing). +Notation Ndiv := N.div (only parsing). +Notation Nmod := N.modulo (only parsing). + +Notation Ndiv_eucl_correct := N.div_eucl_spec (only parsing). +Notation Ndiv_mod_eq := N.div_mod' (only parsing). +Notation Nmod_lt := N.mod_lt (only parsing). |