Definition Para := fun l m =>
    (~ exists X, IncidL X l /\ IncidL X m) /\ exists p, IncidLP l p /\ IncidLP m p.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.

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.