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