Instance Perm_knot : Perm_alg knot :=
Perm_preimage _ _ _ _ unsquash squash squash_unsquash unsquash_squash_join_hom.
Instance Sep_knot(Sep_F: forall A, Sep_alg (F A)) : Sep_alg knot :=
Sep_preimage _ _ _  unsquash squash squash_unsquash unsquash_squash_join_hom.

Lemma join_unsquash : forall x1 x2 x3,
join x1 x2 x3 =
join (unsquash x1) (unsquash x2) (unsquash x3).