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'.