Section T16.
Context `{T2D:Tarski_2D}.
Context `{TE:@Tarski_euclidean Tn TnEQD}.
(** Lemma 16.2 in dimension 2. *)
(** As we are in dimension 2, we skip 16.3 which is only needed to prove 16.4 in dimension n. *)

Lemma exists_coord : forall O E S U P,
S <> U -> Cong O E S U ->
exists PX, exists X, Projp P PX S U /\ Cong_3 O E X S U PX.