proposition: Lemma sams_lea_lta456_suma2__lta123 : forall A B C D E F G H I A' B' C' D' E' F' G' H' I', LtA D' E' F' D E F -> LeA G H I G' H' I' -> SAMS A B C D E F -> SumA A B C D E F G H I -> SumA A' B' C' D' E' F' G' H' I' -> LtA A B C A' B' C'.
proof: Proof. intros A B C D E F G H I A' B' C' D' E' F' G' H' I'. intros. assert_diffs. elim(lea_dec A' B' C' A B C) ;[|intro; apply nlea__lta; auto]. intro Hlea. exfalso. assert(~ LeA G H I G' H' I'); auto. apply lta__nlea. apply(sams_lea_lta456_suma2__lta A' B' C' D' E' F' _ _ _ A B C D E F); auto. Qed.
imports: GeoCoq.Tarski_dev.Ch11_angles