Require Export Bmc.Core.
Definition naive_post (I : prop) (T : trans) (P : prop) (k : nat) : Prop :=
safety_nth I T P (S k).
Definition induction_post (I : prop) (T : trans) (P : prop) : Prop :=
(forall (s:state), I s -> P s) /\
(forall (s s':state), P s -> T s s' -> P s').
(**)

Theorem soundness_naive_bounded :
forall (I:prop) (T:trans) (P:prop) (k:nat),
naive_post I T P k ->
forall (i:nat), i <= (S k) ->
prop_nth_init I T P i.