proposition: Lemma sams_lea2_suma2__lea : forall A B C D E F G H I A' B' C' D' E' F' G' H' I', LeA 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' -> LeA 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' HleaB HleaD Hisi' Hsuma Hsuma'. assert_diffs. assert(Haux := ex_suma A B C D' E' F'). destruct Haux as [G'' [H'' [I'']]]; auto. apply (lea_trans _ _ _ G'' H'' I''). - apply (sams_lea456_suma2__lea A B C D E F _ _ _ D' E' F'); auto. apply (sams_lea2__sams _ _ _ _ _ _ A' B' C' D' E' F'); Lea. - apply (sams_lea123_suma2__lea A B C D' E' F' _ _ _ A' B' C'); auto. Qed.
imports: GeoCoq.Tarski_dev.Ch11_angles