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

Lemma activations_at_rank_incl_activations (rk: nat) (p: cbv) :
incl (activations_at_rank rk p) (activations p).