Open Scope pred.
(* Various utility lemmas *)

(* Specifications: *)
Lemma later_level : forall k1 k2 : K.knot,
laterR k1 k2 ->
level k2 < level k1.
Lemma nec_level : forall k1 k2 : K.knot,
necR k1 k2 ->
level k2 <= level k1.
Lemma age1_level : forall p1 p2 : K.knot,
age1 p1 = Some p2 ->
level p1 = S (level p2).
Lemma later_level : forall k1 k2,
laterR k1 k2 ->
level k2 < level k1.
Lemma nec_level : forall k1 k2,
necR k1 k2 ->
level k2 <= level k1.
Lemma age1_level : forall p1 p2,
age1 p1 = Some p2 ->
level p1 = S (level p2).
Lemma later_level : forall k1 k2 : K.knot,
laterR k1 k2 ->
level k2 < level k1.
Lemma nec_level : forall k1 k2 : K.knot,
necR k1 k2 ->
level k2 <= level k1.