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. *)

Lemma sums_assoc : forall A B C D E F G H I J K L,
SumS A B C D G H -> SumS C D E F I J ->
(SumS G H E F K L <-> SumS A B I J K L).