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_join1 : forall x y z x' : K'.knot, join x y z -> age x x' -> exists y' : K'.knot, exists z' : K'.knot, join x' y' z' /\ age y y' /\ age z z'.