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 knot_age1 : forall k,
age1 k =
match unsquash k with
| (O,_) => None
| (S n,x) => Some (squash (n,x))
end.