proposition: Lemma trisuma_distincts : forall A B C D E F, TriSumA A B C D E F -> A <> B /\ B <> C /\ A <> C /\ D <> E /\ E <> F.
proof: Proof. intros A B C D E F HTri. destruct HTri as [G [H [I [HSuma HSuma1]]]]. apply suma_distincts in HSuma. apply suma_distincts in HSuma1. spliter; repeat split; auto. Qed.
imports: GeoCoq.Tarski_dev.Ch11_angles