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 unage_join2 : forall z x' y' z', join x' y' z' -> age z z' -> exists x, exists y, join x y z /\ age x x' /\ age y y'.