(****************************************************************)
Parameter Apart : Point -> Line -> Prop.
(****************************************************************)
Definition Incident (a : Point) (l : Line) := ~ Apart a l.
Record Segment : Set := Seg
{origin : Point; extremity : Point; Seg_cond : DiPt origin extremity}.
Record Twolines : Set := Twol
{line1 : Line; line2 : Line; Twol_cond : ConLn line1 line2}.
(****************************************************************)
Axiom
line :
forall x : Segment,
{l : Line | Incident (origin x) l /\ Incident (extremity x) l}.
Axiom
point :
forall x : Twolines,
{a : Point | Incident a (line1 x) /\ Incident a (line2 x)}.
(****************************************************************)
Definition ln : Segment -> Line.

Theorem inc_pt1 : forall x : Twolines, Incident (pt x) (line1 x).