proposition: Lemma le_lt12_sums2__lt : forall A B C D E F A' B' C' D' E' F', Lt A B A' B' -> Le C D C' D' -> SumS A B C D E F -> SumS A' B' C' D' E' F' -> Lt E F E' F'.
proof: Proof. intros A B C D E F A' B' C' D' E' F' HLt HLe HSum HSum'. split. apply le2_sums2__le with A B C D A' B' C' D'; Le. intro HCong. destruct HLt as [HLe1 HNCong]. apply HNCong. apply le2_sums2__cong12 with C D E F C' D'; trivial. apply (cong3_sums__sums A' B' C' D' E' F'); Cong. Qed.
imports: GeoCoq.Tarski_dev.Ch06_out_lines