Definition sqrt3 := PythF 1 (PythF 1 1).

Lemma characterization_of_equality_F_aux : forall Ax Ay Bx By,
Ax =F= Bx /\ Ay =F= By <->
(Ax - Bx) * (Ax - Bx) + (Ay - By) * (Ay - By) =F= OF.