Definition flip : Twolines -> Twolines.

(* Specifications: *)
Theorem line1_flip : forall x : Twolines, line1 x = line2 (flip x).
Theorem line2_flip : forall x : Twolines, line2 x = line1 (flip x).
Theorem flip_defines_samept : forall x : Twolines, EqPt (pt x) (pt (flip x)).