(** ABC + 0 =  ABC (two lemmas) *)

(* Specifications: *)
Lemma out546_suma__conga : forall A B C D E F G H I, SumA A B C D E F G H I ->
Out E D F -> CongA A B C G H I.
Lemma out546__suma : forall A B C D E F, A <> B -> B <> C -> Out E D F -> SumA A B C D E F A B C.
(** 0 + DEF = DEF (two lemmas) *)
Lemma out213_suma__conga : forall A B C D E F G H I, SumA A B C D E F G H I ->
Out B A C -> CongA D E F G H I.
Lemma out213__suma : forall A B C D E F, D <> E -> E <> F -> Out B A C -> SumA A B C D E F D E F.
(** Some permutation properties:*)
Lemma suma_left_comm : forall A B C D E F G H I,
SumA A B C D E F G H I -> SumA C B A D E F G H I.
Lemma suma_middle_comm : forall A B C D E F G H I,
SumA A B C D E F G H I -> SumA A B C F E D G H I.
Lemma suma_right_comm : forall A B C D E F G H I,
SumA A B C D E F G H I -> SumA A B C D E F I H G.
Lemma suma_comm : forall A B C D E F G H I,
SumA A B C D E F G H I -> SumA C B A F E D I H G.