Variant rot_to_arc_spec p x y :=
RotToArcSpec i p1 p2 of x :: p1 = arc p x y
& y :: p2 = arc p y x
& rot i p = x :: p1 ++ y :: p2 :
rot_to_arc_spec p x y.

Lemma rot_to_arc p x y :
uniq p -> x \in p -> y \in p -> x != y -> rot_to_arc_spec p x y.