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' *)

Lemma sams_lea_lta123_suma2__lta456 : forall A B C D E F G H I A' B' C' D' E' F' G' H' I',
LtA A' B' C' A B C -> LeA G H I G' H' I' -> SAMS A B C D E F ->
SumA A B C D E F G H I -> SumA A' B' C' D' E' F' G' H' I' -> LtA D E F D' E' F'.