Ltac vard_unfold :=
unfold runHandler,
getk,
setk,
delk,
resp in *; monad_unfold.

Lemma trace_state_correct_trace_correct :
forall st st' st'' trace t,
trace_state_correct trace st st' ->
trace_correct' st trace ->
step_1 st' st'' t ->
trace_correct' st (trace ++ t).