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'.