Proof using.
unfold outputs_1. auto using map_app.
Qed.

Lemma processInputs_app :
forall l1 l2 d,
processInputs d (l1 ++ l2) = let (d', os) := processInputs d l1 in
let (d'', os') := processInputs d' l2 in
(d'', os ++ os').