From Undecidability.L Require Import LTactics.
Fixpoint many_lam k s := match k with 0 => s | S k => lam (many_lam k s) end.
Fixpoint many_app k s (v : Vector.t term k) :=
match v with
| Vector.nil => s
| Vector.cons x _ v => many_app (L.app s x) v
end.

Lemma equiv_many_app_L k (v : Vector.t term k) s t :
s == t -> many_app s v == many_app t v.