Section Common.
Variable f : K1.knot -> K2.knot.
Variable g : K2.knot -> K1.knot.
Definition f_pred' (p1 : K1.predicate) : K2.predicate :=
p1 oo map_pair g (@id other).
Definition g_pred' (p2 : K2.predicate) : K1.predicate :=
p2 oo map_pair f (@id other).
Variable f_level : forall k, level k = level (f k).
Variable g_level : forall k, level k = level (g k).

Lemma f_pred'_approx: forall n,
f_pred' oo K1.approx n = K2.approx n oo f_pred'.