Ndiv_def.v

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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.a, b:positive
snd (Pdiv_eucl a b) < N.pos b
Proof.a, b:positive
snd (Pdiv_eucl a b) < N.pos b now apply (N.pos_div_eucl_remainder a (Npos b)). Qed.

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).