Proof (proj2 (Pos2Nat.inj_gt p q)).
(** Old intermediate results about [Pmult_nat] *)
Section ObsoletePmultNat.

(* Specifications: *)
Lemma Pmult_nat_mult : forall p n,
Pmult_nat p n = Pos.to_nat p * n.
Lemma Pmult_nat_succ_morphism :
forall p n, Pmult_nat (Pos.succ p) n = n + Pmult_nat p n.
Theorem Pmult_nat_l_plus_morphism :
forall p q n, Pmult_nat (p + q) n = Pmult_nat p n + Pmult_nat q n.
Theorem Pmult_nat_plus_carry_morphism :
forall p q n, Pmult_nat (Pos.add_carry p q) n = n + Pmult_nat (p + q) n.
Lemma Pmult_nat_r_plus_morphism :
forall p n, Pmult_nat p (n + n) = Pmult_nat p n + Pmult_nat p n.
Lemma ZL6 : forall p, Pmult_nat p 2 = Pos.to_nat p + Pos.to_nat p.
Lemma le_Pmult_nat : forall p n, n <= Pmult_nat p n.
End ObsoletePmultNat.