Section T8_4.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.
(** This following result is very important, it shows the existence of a midpoint. The proof is involved because we are not using continuity axioms. *)
(** This corresponds to l8_22 in Tarski's book. *)

Lemma perp_in_perp : forall A B C D X, Perp_at X A B C D -> Perp A B C D.