(****************************************************************)
Axiom
el_ax :
forall (x : Segment) (l m : Line),
DiLn l m ->
(Apart (origin x) l \/ Apart (extremity x) l) \/
Apart (origin x) m \/ Apart (extremity x) m.
Axiom
cmp_apt_dipt :
forall (a b : Point) (l : Line), Apart a l -> DiPt a b \/ Apart b l.
Axiom
cmp_apt_diln :
forall (a : Point) (l m : Line), Apart a l -> DiLn l m \/ Apart a m.

Axiom cmp_con_diln : forall l m n : Line, ConLn l m -> DiLn m n \/ ConLn l n.
Record Triangle : Set := Tri
{summit : Point; base : Segment; Tri_cond : Apart summit (ln base)}.