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 bimap_bimap : forall A B C X Y Z (s:X->Y) (t:Y->Z) (f:B->C) (g:A->B) x, bimap s f (bimap t g x) = bimap (t oo s) (f oo g) x.