(** Basic properties about the sum of the angles of a triangle *)

(* Specifications: *)
Lemma ex_trisuma : forall A B C, A <> B -> B <> C -> A <> C ->
exists D E F, TriSumA A B C D E F.
Lemma trisuma_perm_231 : forall A B C D E F, TriSumA A B C D E F -> TriSumA B C A D E F.
Lemma trisuma_perm_312 : forall A B C D E F, TriSumA A B C D E F -> TriSumA C A B D E F.
Lemma trisuma_perm_321 : forall A B C D E F, TriSumA A B C D E F -> TriSumA C B A D E F.
Lemma trisuma_perm_213 : forall A B C D E F, TriSumA A B C D E F -> TriSumA B A C D E F.
Lemma trisuma_perm_132 : forall A B C D E F, TriSumA A B C D E F -> TriSumA A C B D E F.
Lemma conga_trisuma__trisuma : forall A B C D E F D' E' F',
TriSumA A B C D E F -> CongA D E F D' E' F' -> TriSumA A B C D' E' F'.
Lemma trisuma2__conga : forall A B C D E F D' E' F',
TriSumA A B C D E F -> TriSumA A B C D' E' F' -> CongA D E F D' E' F'.
Lemma conga3_trisuma__trisuma : forall A B C D E F A' B' C', TriSumA A B C D E F ->
CongA A B C A' B' C' -> CongA B C A B' C' A' -> CongA C A B C' A' B' ->
TriSumA A' B' C' D E F.