Global Instance IncidLP_morphisml : Proper(EqL ==> eq ==> iff) IncidLP.Global Instance IncidLP_morphismr : Proper(eq ==> EqP ==> iff) IncidLP.

(* Specifications: *)
Lemma same_side__plane : forall A B l, same_side A B l -> exists p, IncidP A p /\ IncidP B p /\ IncidLP l p.
Lemma same_side_prime__plane : forall A B C D, same_side' A B C D -> exists p, IncidP A p /\ IncidP B p /\ IncidP C p /\ IncidP D p.
Lemma cut_same_side_cut : forall P X Y l, cut l P X -> same_side X Y l -> cut l P Y.
Lemma isosceles_congaH : forall A B C, ~ColH A B C -> CongH A B A C -> CongaH A B C A C B.
Lemma cong_distincts : forall A B C D, A <> B -> Cong A B C D -> C <> D.
Lemma cong_sym : forall A B C D, Cong A B C D -> Cong C D A B.
Lemma cong_trans : forall A B C D E F, Cong A B C D -> Cong C D E F -> Cong A B E F.
Lemma betH_not_congH : forall A B C, BetH A B C -> ~ CongH A B A C.
Lemma congH_permlr : forall A B C D, A<>B -> C<>D -> CongH A B C D -> CongH B A D C.
Lemma congH_perms : forall A B C D, A<>B -> C<>D -> CongH A B C D -> (CongH B A C D /\ CongH A B D C /\ CongH C D A B /\ CongH D C A B /\ CongH C D B A /\ CongH D C B A /\ CongH B A D C).
Lemma congH_perml : forall A B C D, A <> B -> C <> D -> CongH A B C D -> CongH B A C D.
Lemma bet_cong3_bet : forall A B C A' B' C', A' <> B' -> B' <> C' -> A' <> C' -> BetH A B C -> ColH A' B' C' -> CongH A B A' B' -> CongH B C B' C' -> CongH A C A' C' -> BetH A' B' C'.
Lemma betH_congH3_outH_betH : forall A B C A' B' C', BetH A B C -> outH A' B' C' -> CongH A C A' C' -> CongH A B A' B' -> BetH A' B' C'.
Lemma outH_sym : forall A B C, A <> C -> outH A B C -> outH A C B.
Lemma soustraction_betH : forall A B C A' B' C' : Point, BetH A B C -> BetH A' B' C' -> CongH A B A' B' -> CongH A C A' C' -> CongH B C B' C'.
Lemma ncolH_expand : forall A B C, ~ ColH A B C -> ~ ColH A B C /\ A <> B /\ B <> C /\ A <> C.
Lemma betH_outH__outH : forall A B C D, BetH A B C -> outH B C D -> outH A C D.
Lemma th12: forall A B C A' B' C', ~ ColH A B C -> ~ ColH A' B' C' -> CongH A B A' B' -> CongH A C A' C' -> CongaH B A C B' A' C' -> CongaH A B C A' B' C' /\ CongaH A C B A' C' B' /\ CongH B C B' C'.
Lemma th14: forall A B C D A' B' C' D', ~ ColH A B C -> ~ ColH A' B' C' -> CongaH A B C A' B' C' -> BetH A B D -> BetH A' B' D' -> CongaH C B D C' B' D'.
Lemma congH_colH_betH: forall A B I, A<>B -> A<>I -> B<>I -> CongH I A I B -> ColH I A B -> BetH A I B.