proposition: Lemma sams_lea_lta789_suma2__lta123 : forall A B C D E F G H I A' B' C' D' E' F' G' H' I', LeA D' E' F' D E F -> LtA 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 Hlta. exfalso. assert(~ LtA G H I G' H' I'); auto. apply lea__nlta. apply(sams_lea2_suma2__lea A' B' C' D' E' F' _ _ _ A B C D E F); auto. Qed.
imports: GeoCoq.Tarski_dev.Ch11_angles