(* Axiom unsquash_inj : forall k1 k2, unsquash k1 = unsquash k2 -> k1 = k2. Arguments unsquash_inj [k1 k2] _.  Axiom squash_surj : forall k, exists n, exists Fp, squash (n, Fp) = k.  Axiom unsquash_approx : forall k n Fp, unsquash k = (n, Fp) -> Fp = KI.fmap (approx n) Fp. Implicit Arguments unsquash_approx [k n Fp].  Axiom approx_approx1 : forall m n, approx n = approx n oo approx (m+n).  Axiom approx_approx2 : forall m n, approx n = approx (m+n) oo approx n. *)
End KNOT__COVARIANT_HERED_PROP_OTH.
Module Type KNOT_INPUT__COVARIANT_HERED_PROP.
Parameter F : functor.
End KNOT_INPUT__COVARIANT_HERED_PROP.
Module Type KNOT__COVARIANT_HERED_PROP.
Declare Module KI : KNOT_INPUT__COVARIANT_HERED_PROP.
Parameter knot : Type.
Parameter ageable_knot : ageable knot.
Existing Instance ageable_knot.
Parameter squash : (nat * F (pred knot)) -> knot.
Parameter unsquash : knot -> (nat * F (pred knot)).
Parameter approx : nat -> pred knot -> pred knot.

(* Definitions of the "ageable" operations *)
Axiom knot_level : forall (k:knot),
level k = fst (unsquash k).