(** 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 five_segment : forall A A' B B' C C' D D',
CongM A B A' B' ->
CongM B C B' C' ->
CongM A D A' D' ->
CongM B D B' D' ->
BetM A B C -> BetM A' B' C' -> A <> B ->
CongM C D C' D'.