Module Type KNOT_HERED.
Declare Module TF:TY_FUNCTOR_PROP.
Parameter knot:Type.
Parameter ag_knot : ageable knot.
Existing Instance ag_knot.
Existing Instance ag_prod.
Definition predicate := pred (knot * other).
Parameter squash : (nat * F predicate) -> knot.
Parameter unsquash : knot -> (nat * F predicate).
Parameter approx : nat -> predicate -> predicate.

Axiom squash_unsquash : forall k:knot, squash (unsquash k) = k.
Axiom unsquash_squash : forall (n:nat) (f:F predicate),
unsquash (squash (n,f)) = (n, fmap F (approx n) f).