Section Sums.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.
(** Existence of the sum *)
(** Commutativity of the sum. *)
(** Unicity of the sum. *)
(** Unicity of the difference of segments. *)
(** Unicity of the difference of segments on the right. *)
(** Cong preserves SumS *)
(** The degenerate segments represent the additive identity *)
(** Some permutation properties *)
(** Basic case of sum *)
(** Associativity of the sum. *)
(** AB <= AB + CD *)
(** CD <= AB + CD *)
(** If the sum of two segments is degenerate, then the segments are degenerate *)

Lemma eq_sums__eq : forall A B C D E, SumS A B C D E E -> A = B /\ C = D.