(** AB <= AB + CD *)

(* Specifications: *)
Lemma sums__le1256 : forall A B C D E F, SumS A B C D E F -> Le A B E F.
(** CD <= AB + CD *)
Lemma sums__le3456 : forall A B C D E F, SumS A B C D E F -> Le C D E F.
(** If the sum of two segments is degenerate, then the segments are degenerate *)
Lemma eq_sums__eq : forall A B C D E, SumS A B C D E E -> A = B /\ C = D.
Lemma sums_diff_1 : forall A B C D E F, A <> B -> SumS A B C D E F -> E <> F.
Lemma sums_diff_2 : forall A B C D E F, C <> D -> SumS A B C D E F -> E <> F.
(** SumS preserves Le *)
Lemma le2_sums2__le : forall A B C D E F A' B' C' D' E' F',
Le A B A' B' -> Le C D C' D' -> SumS A B C D E F -> SumS A' B' C' D' E' F' ->
Le E F E' F'.