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) *)
(** If x>90 then x+x>180. *)
(** If x+x<180 then x<90. *)
(** If x+x>180 then x>90. *)
(** If doubling two acute angles makes the same result, then these angles are congruent *)
(** Sum of two straight angles is a null angle *)
(** Sum of two degenerate angles is degenerate *)
(** The sum of two supplementary angles is a flat angle (two lemmas) *)
(** If the sum of two angles is a flat angle, then they are supplementary *)
(** The sum of two angles is equal to the sum of their two supplementary angles *)
(** If doubling two obtuse angles makes the same result, then these angles are congruent *)
(** If doubling two angles makes the same result, then they are either congruent or supplementary *)

Lemma bet_suma2__or_conga : forall A B C D E F A' B' C' A0, A0 <> B ->
Bet A B A0 -> SumA A B C A B C D E F -> SumA A' B' C' A' B' C' D E F ->
CongA A B C A' B' C' \/ CongA A0 B C A' B' C'.