Definition inductive (step : step_relation) (P : A -> Prop)  :=
    forall (a a': A) (os : list trace),
      P a ->
      step a a' os ->
      P a'.

Theorem step_star_inductive : forall step P, inductive step P -> forall (a : A) a' os, P a -> (refl_trans_1n_trace step) a a' os -> P a'.