Definition shorter_ss_l (ss1 ss2 : sseq) (o i: nat) : Prop :=
forall (j : nat), j <= i-o -> ss1.[i-j] = ss2.[i-j].
Definition shorter_ss_u (ss1 ss2 : sseq) (i d: nat) : Prop :=
forall (j : nat), ss1.[i+j+d] = ss2.[i+j].
Definition shorter_ss (ss1 ss2 : sseq) (o i d: nat) : Prop :=
shorter_ss_l ss1 ss2 o i /\ shorter_ss_u ss1 ss2 i d.

Lemma not_no_loop'_eq_states :
forall (j o i:nat) (ss:sseq),
~ no_loop' ss o i j ->
~(forall (k:nat), k > j \/ ss.[o+i] <> ss.[o+k]).