Section Suma_2.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.
(** ABC <= ABC + DEF. *)
(** DEF <= ABC + DEF. *)
(** LeA preserves SAMS. *)
(** SumA preserves LeA. *)
(** Unicity of the difference of angles. *)
(** Unicity of the difference on the left. *)
(** Associativity of the sum of angles. *)
(** If B <= B', E <= E' and B + E = B' + E', then B = B' and E = E' *)
(** If B + E = E, then B = 0 *)
(** If B < B' and E <= E', then B + E < B' + E' *)
(** If E >= E' and B + E <= B' + E', then B <= B' *)
(** If E > E' and B + E <= B' + E', then B < B' *)
(** If E >= E' and B + E < B' + E', then B < B' *)
(** The sum of two angles of a triangle is less than a straight angle (three lemmas) *)
(** Sum of two right angles is a straight angle: 90+90=180. *)
(** If 90+x=180 then x=90. *)
(** If x+90=180 then x=90. *)
(** If x+x=180 then x=90. *)
(** If x<90 then x+x<180 (two lemmas). *)
(** If x<90 and y<90 then x+y<180 (two lemmas). *)
(** If x<90 then x+90<180 (two lemmas) *)

Lemma acute_per__sams : forall A B C D E F, A <> B -> B <> C ->
Per A B C -> Acute D E F -> SAMS A B C D E F.