Definition ParaP := fun A B C D =>
forall l m, IncidL A l -> IncidL B l -> IncidL C m -> IncidL D m -> Para l m.

(* Specifications: *)
Lemma segment_constructionH : forall A B C D : Point,
A <> B -> C <> D -> exists E : Point, BetH A B E /\ CongH B E C D.
Lemma EqL_dec : forall l m, EqL l m \/ ~EqL l m.
Definition is_line A B l := A <> B /\ IncidL A l /\ IncidL B l.
Lemma cut_exists : forall A l, ~IncidL A l -> exists B, cut l A B.
Lemma outH_col : forall A B C, outH A B C -> ColH A B C.
intros.