proposition: Theorem eq_strong_ps_mul_compat_r : ∀ ps₁ ps₂ ps₃, eq_ps_strong ps₁ ps₂ → eq_ps_strong (ps_mul ps₁ ps₃) (ps_mul ps₂ ps₃).
proof: Proof. intros ps₁ ps₂ ps₃ Heq. induction Heq. constructor; simpl. rewrite H, H0; reflexivity. unfold cm; simpl. rewrite H0; reflexivity. unfold cm_factor. rewrite H0, H1. reflexivity. Qed.
imports: Utf8 QArith NPeano Misc NbarM Field2 Fsummation Power_series Puiseux_series Ps_add Ps_add_compat