(* Proposition 7 *)
Definition activations_at_rank (rk: nat) (p : cbv) : list cbv :=
filter (fun p => beq_nat rk (activation_rank rank p)) (activations p).

(* Specifications: *)
Lemma activations_at_rank_incl_activations (rk: nat) (p: cbv) :
incl (activations_at_rank rk p) (activations p).
Lemma activations_at_rank_wf (rk: nat) (p p': cbv) :
wf p ->
In p' (activations_at_rank rk p) ->
wf p'.