Require Export GeoCoq.Tarski_dev.Ch14_order.
Section T15.
Context `{T2D:Tarski_2D}.
Context `{TE:@Tarski_euclidean Tn TnEQD}.
(** Lemma 15.2 *)
(** Cong corresponds to length equality.*)
(** Le corresponds to length inequality.*)

Lemma triangular_equality_equiv :
(forall O E A , O<>E -> (forall E' B C AB BC AC,
Bet A B C ->
Length O E E' A B AB -> Length O E E' B C BC -> Length O E E' A C AC ->
Sum O E E' AB BC AC)) <->
(forall O E E' A B C AB BC AC,
O<>E -> Bet A B C ->
Length O E E' A B AB -> Length O E E' B C BC -> Length O E E' A C AC ->
Sum O E E' AB BC AC).