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