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 pythagoras : forall O E E' A B C AC BC AB AC2 BC2 AB2,
O <> E -> Per A C B ->
Length O E E' A B AB ->
Length O E E' A C AC ->
Length O E E' B C BC ->
Prod O E E' AC AC AC2 ->
Prod O E E' BC BC BC2 ->
Prod O E E' AB AB AB2 ->
Sum  O E E' AC2 BC2 AB2.