Library Coq.NArith.Ndiv_def

Require Import BinNat.
Local Open Scope N_scope.

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 Ndiv_eucl := N.div_eucl (compat "8.3").
Notation Ndiv := N.div (compat "8.3").
Notation Nmod := N.modulo (compat "8.3").

Notation Ndiv_eucl_correct := N.div_eucl_spec (compat "8.3").
Notation Ndiv_mod_eq := N.div_mod´ (compat "8.3").
Notation Nmod_lt := N.mod_lt (compat "8.3").