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 core_unsquash : forall x, core x = squash (core (unsquash x)).