(** Characterization of SAMS using LeA. *)

(* Specifications: *)
Lemma sams_chara : forall A B C D E F A', A<>B -> A'<>B -> Bet A B A' ->
(SAMS A B C D E F <-> LeA D E F C B A').
Lemma sams_distincts : forall A B C D E F, SAMS A B C D E F ->
A<>B /\ B<>C /\ D<>E /\ E<>F.
Lemma sams_sym : forall A B C D E F, SAMS A B C D E F ->
SAMS D E F A B C.
Lemma sams_right_comm : forall A B C D E F, SAMS A B C D E F ->
SAMS A B C F E D.
Lemma sams_left_comm : forall A B C D E F, SAMS A B C D E F ->
SAMS C B A D E F.
Lemma sams_comm : forall A B C D E F, SAMS A B C D E F ->
SAMS C B A F E D.
Lemma conga2_sams__sams : forall A B C D E F A' B' C' D' E' F',
CongA A B C A' B' C' -> CongA D E F D' E' F' ->
SAMS A B C D E F -> SAMS A' B' C' D' E' F'.
Lemma out546__sams : forall A B C D E F, A <> B -> B <> C -> Out E D F -> SAMS A B C D E F.
Lemma out213__sams : forall A B C D E F, D <> E -> E <> F -> Out B A C -> SAMS A B C D E F.
Lemma bet_suma__sams : forall A B C D E F G H I, SumA A B C D E F G H I -> Bet G H I ->
SAMS A B C D E F.
Lemma bet__sams : forall A B C P, A <> B -> B <> C -> P <> B -> Bet A B C -> SAMS A B P P B C.
Lemma suppa__sams : forall A B C D E F, SuppA A B C D E F -> SAMS A B C D E F.
Lemma inangle__sams : forall A B C P, InAngle P A B C -> SAMS A B P P B C.
End Suma_1.