proposition: Lemma Smorph_opp x : [-!x] == -[x].
proof: Proof. rewrite <- (Radd_0_l Rth [-!x]). rewrite <- ((Ropp_def Rth) [x]). rewrite ((Radd_comm Rth) [x]). rewrite <- (Radd_assoc Rth). rewrite <- (Smorph_add Smorph). rewrite (Ropp_def Cth). rewrite (Smorph0 Smorph). rewrite (Radd_comm Rth (-[x])). now apply (Radd_0_l Rth). Qed.
imports: Setoid Morphisms BinPos BinNat