Inductive point : Set :=
| Point : nat -> nat -> point.

Inductive line : Set :=
| Line : point -> point -> line.

Inductive plane : Set :=
(* Plane through 3 non-collinear points *)
| Plane3Pt : point -> point -> point -> plane.

Definition projX (a:point) : nat :=
  match a with
  | Point x _ => x
  end.
Definition projY (a:point) : nat :=
  match a with
  | Point _ y => y
  end.