Definition ageable_knot : ageable knot :=
    mkAgeable knot knot_level_def knot_age1_def ag_knot_facts.Definition knot_rel (k1 k2:knot) :=
    let (n,f) := unsquash k1 in
    let (n',f') := unsquash k2 in
    n = n' /\ Rel predicate predicate f f'.

Lemma hered_spec : forall p, hered p = (forall k k' k'' o o', clos_refl_trans _ age k k' -> knot_rel k' k'' -> ORel o o' -> T_rel (p (k,o)) (p (k'',o'))).