(****************************************************************)

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)}.(****************************************************************)

Record Triangle : Set := Tri
  {summit : Point; base : Segment; Tri_cond : Apart summit (ln base)}.(****************************************************************)

Record Triangle : Set := Tri
  {summit : Point; base : Segment; Tri_cond : Apart summit (ln base)}.(****************************************************************)

Record Triangle : Set := Tri
  {summit : Point; base : Segment; Tri_cond : Apart summit (ln base)}.(****************************************************************)

Record Triangle : Set := Tri
  {summit : Point; base : Segment; Tri_cond : Apart summit (ln base)}.

Theorem Triangle_def : forall t : Triangle, Apart (summit t) (ln (base t)).