Instance Perm_knot : Perm_alg knot :=
    Perm_preimage _ _ _ _ unsquash squash squash_unsquash unsquash_squash_join_hom.Instance Sep_knot: Sep_alg knot :=
    Sep_preimage _ _ _  unsquash squash squash_unsquash unsquash_squash_join_hom.

Lemma age_join2 : forall x y z z' : K'.knot, join x y z -> age z z' -> exists x' : K'.knot, exists y' : K'.knot, join x' y' z' /\ age x x' /\ age y y'.