proposition: Lemma Rplus_eq_0 : forall r1 r2, 0 <= r1 -> 0 <= r2 -> r1 + r2 = 0 -> r1 = 0 /\ r2 = 0.
proof: Proof. intros r1 r2 H1 H2 Hp; split. - now apply (Rplus_eq_0_l _ r2). - now rewrite Rplus_comm in Hp; apply (Rplus_eq_0_l r2 r1). Qed.
imports: RelationClasses Raxioms Rpow_def ZArith ZArithRing RealField