Module KI:=KI'.Definition F : functor :=
      CoContraVariantBiFunctor_MixVariantFunctor KI.F.Definition other := KI.other.Definition Rel (A: Type): F A -> F A -> Prop :=
      KI.Rel A A.Definition Rel_fmap (A B: Type): forall (f1: A->B) (f2:B->A) x y,
      Rel A x y ->
      Rel B (fmap F f1 f2 x) (fmap F f1 f2 y) :=
    KI.Rel_fmap A B B A.Definition Rel_refl (A: Type): forall x, Rel A x x :=
      KI.Rel_refl A A.Definition Rel_trans (A: Type): forall x y z,
      Rel A x y -> Rel A y z -> Rel A x z :=
      KI.Rel_trans A A.Definition ORel: other -> other -> Prop := KI.ORel.Definition ORel_refl := KI.ORel_refl.Definition ORel_trans := KI.ORel_trans.Definition T := KI.T.Definition T_bot := KI.T_bot.Definition T_rel := KI.T_rel.Definition T_rel_bot := KI.T_rel_bot.Definition T_rel_refl := KI.T_rel_refl.Definition T_rel_trans := KI.T_rel_trans.Module K := knot_full_variant.Knot_MixVariantHeredTOthRel(Input).Definition knot: Type := K.knot.Definition ageable_knot: ageable knot := K.ageable_knot.Definition hered : (knot * KI.other -> KI.T) -> Prop := K.hered.Definition predicate := { p:knot * KI.other -> KI.T | hered p }.Definition squash : (nat * KI.F predicate predicate) -> knot := K.squash.Definition unsquash : knot -> (nat * KI.F predicate predicate) := K.unsquash.Definition approx : nat -> predicate -> predicate := K.approx.Definition squash_unsquash : forall k:knot, squash (unsquash k) = k
    := K.squash_unsquash.Definition unsquash_squash : forall (n:nat) (f:KI.F predicate predicate),
    unsquash (squash (n,f)) =
     (n, CoContraVariantBiFunctor.fmap KI.F (approx n) (approx n) f)
    := K.unsquash_squash.Definition approx_spec : forall n p ko,
    proj1_sig (approx n p) ko =
     if (le_gt_dec n (level (fst ko))) then KI.T_bot else proj1_sig p ko
    := K.approx_spec.Definition knot_rel (k1 k2:knot) :=
    let (n,f) := unsquash k1 in
    let (n',f') := unsquash k2 in
    n = n' /\ KI.Rel predicate predicate f f'.Definition knot_age1 : forall k:knot,
    age1 k =
    match unsquash k with
    | (O,_) => None
    | (S n,x) => Some (squash (n,x))
    end
    := K.knot_age1.Definition knot_level : forall k:knot,
    level k = fst (unsquash k)
    := K.knot_level.Definition hered_spec : forall p,
    hered p =
    (forall k k' k'' o o',
      clos_refl_trans _ age k k' ->
      knot_rel  k' k'' ->
      KI.ORel o o' ->
      KI.T_rel (p (k,o)) (p (k'',o')))
    := K.hered_spec.

Lemma approx_approx2 : forall m n, approx n = approx (m+n) oo approx n.