(** 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.

(* Specifications: *)
Lemma Mcong_reflexivity : forall A B,
CongM A B A B.
Lemma Mcong_symmetry : forall A B C D ,
CongM A B C D -> CongM C D A B.
Lemma between_trivial : forall A B, BetM A B B.
Lemma Mcong_trivial_identity : forall A B, CongM A A B B.
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.
Lemma cong_pre_pseudo_reflexivity : forall A B C D,
C <> D -> BetM D C B -> CongM A B B A.
Lemma cong_pseudo_reflexivity : forall A B, CongM A B B A.
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'.