Definition knot_rel (k1 k2:knot) :=
let (n,f) := unsquash k1 in
let (n',f') := unsquash k2 in
n = n' /\ Rel predicate f f'.

Axiom hered_spec : forall p,
hered p =
(forall k k' k'' o o',
clos_refl_trans _ age k k' ->
knot_rel  k' k'' ->
ORel o o' ->
T_rel (p (k,o)) (p (k'',o'))).