Module Type ISOMORPHIC_KNOTS.
Declare Module TF : TY_FUNCTOR.
Declare Module K1 : KNOT with Module TF := TF.
Declare Module K2 : KNOT with Module TF := TF.
Parameter f : K1.knot -> K2.knot.
Parameter g : K2.knot -> K1.knot.
Definition fF : F K1.predicate -> F K2.predicate :=
fmap F (fun p : K1.knot * other -> K1.TF.T => p oo map_pair g (@id other)).
Definition gF : F K2.predicate -> F K1.predicate :=
fmap F (fun p : K2.knot * other -> K2.TF.T => p oo map_pair f (@id other)).

Axiom f_squash : forall n F1,
f (K1.squash (n, F1)) = K2.squash (n, fF F1).