proposition: Lemma sams_lea_lta123_suma2__lta : forall A B C D E F G H I A' B' C' D' E' F' G' H' I', LtA A B C A' B' C' -> LeA D E F D' E' F' -> 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 G H I G' H' I'.
proof: Proof. intros A B C D E F G H I A' B' C' D' E' F' G' H' I' HltaB HleaE Hisi' Hsuma Hsuma'. assert_diffs. split. apply (sams_lea2_suma2__lea A B C D E F _ _ _ A' B' C' D' E' F'); Lea. intro. destruct HltaB as [HleaB HNConga]. apply HNConga. apply (sams_lea2_suma2__conga123 _ _ _ D E F G H I _ _ _ D' E' F'); auto. apply (conga3_suma__suma A' B' C' D' E' F' G' H' I'); CongA. Qed.
imports: GeoCoq.Tarski_dev.Ch11_angles