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 thales : forall O E E' P A B C D A1 B1 C1 D1 AD,
O <> E -> Col P A B -> Col P C D -> ~ Col P A C -> Pj A C B D ->
Length O E E' P A A1 -> Length O E E' P B B1 ->
Length O E E' P C C1 -> Length O E E' P D D1 ->
Prodg O E E' A1 D1 AD ->
Prodg O E E' C1 B1 AD.