proposition: Lemma per2__sams : forall A B C D E F, A <> B -> B <> C -> D <> E -> E <> F -> Per A B C -> Per D E F -> SAMS A B C D E F.
proof: Proof. intros A B C D E F HAB HBC HDE HEF HPerB HPerE. destruct (ex_suma A B C D E F) as [G [H [I]]]; auto. apply bet_suma__sams with G H I; [|apply (per2_suma__bet A B C D E F)]; assumption. Qed.
imports: GeoCoq.Tarski_dev.Ch11_angles