(** In this file we formalize the result given in T. J. M. Makarios: A further simplification of Tarski's axioms of geometry, June 2013. *)
Section Makarios_variant_to_Tarski83.
Context `{MTn:Tarski_neutral_dimensionless_variant_with_decidable_point_equality}.
Ltac prolong A B x C D :=
assert (sg:= Msegment_construction A B C D);
ex_and sg x.

Lemma LmCoghGrab : forall A B C D E F,
A <> B -> BetM B A C -> BetM D A E ->
CongM B A D A -> CongM A C A E -> CongM B F D F ->
CongM F C E F.