- rewrite nat_of_P_mult_morphism; auto with real.
- rewrite nat_of_P_mult_morphism; auto with real.
rewrite Rmult_comm.
rewrite Ropp_mult_distr_l_reverse; auto with real.
apply Ropp_eq_compat; rewrite mult_comm; auto with real.
- rewrite nat_of_P_mult_morphism; auto with real.
rewrite Ropp_mult_distr_l_reverse; auto with real.
- rewrite nat_of_P_mult_morphism; auto with real.
rewrite Rmult_opp_opp; auto with real.
Qed.

(* Specifications: *)
Theorem absolu_Zs :
forall z : Z, (0 <= z)%Z -> Zabs_nat (Zsucc z) = S (Zabs_nat z).