(* Lemma extends_fashionable : forall x y, R_extends x y -> fashionR x y. *)

(* Specifications: *)
Lemma knot_contracts_age_commute1 : forall x y z,
age x y /\ knot_contracts y z -> exists y',
knot_contracts x y' /\ age y' z.
Lemma knot_contracts_age_commute2 : forall x y z,
knot_contracts x y /\ age y z -> exists y',
age x y' /\ knot_contracts y' z.