proposition: Lemma Rplus_eq_0_l : forall r1 r2, 0 <= r1 -> 0 <= r2 -> r1 + r2 = 0 -> r1 = 0.
proof: Proof. intros r1 r2 [Hlt | <-]; try easy. intros [Hlt' | <-] H. - exfalso; apply (Rgt_not_eq (r1 + r2) 0); try easy. now rewrite <-(Rplus_0_r 0); apply Rplus_lt_compat. - now rewrite Rplus_0_r in H. Qed.
imports: RelationClasses Raxioms Rpow_def ZArith ZArithRing RealField