Require Export Bmc.Core.
Definition k_ind_step (T : trans)
(P : prop) (i: nat) : Prop :=
forall ss : sseq,
path T ss 0 i -> safety_nth_offset P ss 0 i -> P ss.[i].
Definition k_induction_post (I : prop) (T : trans) (P : prop) (k: nat) : Prop :=
k_ind_step T P (S k) /\ safety_nth I T P k.
(**)

Lemma cons_safety_nth_offset : forall (P : prop) (ss : sseq) (i j : nat),
P ss.[i] /\ safety_nth_offset P ss (S i) j <->
safety_nth_offset P ss i (S j).