Ltac myinv :=
match goal with
| [ H: False |- _ ] => destruct H
| [ H: _ /\ _ |- _ ] => destruct H; myinv
| [ H: exists _, _ |- _ ] => destruct H; myinv
| _ => idtac
end.

(* Specifications: *)
Theorem step_expr_sound:
forall a k m, reducts_ok k a m (step_expr k a m)
with step_exprlist_sound:
forall al m, list_reducts_ok al m (step_exprlist al m).