The Coq Proof Assistant

# Library Coq.NArith.Ndiv_def

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.
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).