Fixpoint fold_Ssequence lc :=
  match lc with
  | nil => Sskip
  | c1 :: nil => c1
  | c :: lc0 => Ssequence c (fold_Ssequence lc0)
  end.Definition non_Sseq c :=
  match c with
  | Ssequence _ _ => False
  | _ => True
  end.Inductive unfold_Sseq_rel: statement -> list statement -> Prop :=
  | singleton: forall c, non_Sseq c -> unfold_Sseq_rel c (c :: nil)
  | tl_step: forall c1 c2 lc, non_Sseq c1 -> unfold_Sseq_rel c2 lc ->
                 unfold_Sseq_rel (Ssequence c1 c2) (c1 :: lc)
  | hd_step: forall c1 c2 c3 lc, unfold_Sseq_rel (Ssequence c1 (Ssequence c2 c3)) lc ->
                 unfold_Sseq_rel (Ssequence (Ssequence c1 c2) c3) lc
  .Inductive unfold_Sseq_rel: statement -> list statement -> Prop :=
  | singleton: forall c, non_Sseq c -> unfold_Sseq_rel c (c :: nil)
  | tl_step: forall c1 c2 lc, non_Sseq c1 -> unfold_Sseq_rel c2 lc ->
                 unfold_Sseq_rel (Ssequence c1 c2) (c1 :: lc)
  | hd_step: forall c1 c2 c3 lc, unfold_Sseq_rel (Ssequence c1 (Ssequence c2 c3)) lc ->
                 unfold_Sseq_rel (Ssequence (Ssequence c1 c2) c3) lc
  .Inductive unfold_Sseq_rel: statement -> list statement -> Prop :=
  | singleton: forall c, non_Sseq c -> unfold_Sseq_rel c (c :: nil)
  | tl_step: forall c1 c2 lc, non_Sseq c1 -> unfold_Sseq_rel c2 lc ->
                 unfold_Sseq_rel (Ssequence c1 c2) (c1 :: lc)
  | hd_step: forall c1 c2 c3 lc, unfold_Sseq_rel (Ssequence c1 (Ssequence c2 c3)) lc ->
                 unfold_Sseq_rel (Ssequence (Ssequence c1 c2) c3) lc
  .Inductive unfold_Sseq_rel: statement -> list statement -> Prop :=
  | singleton: forall c, non_Sseq c -> unfold_Sseq_rel c (c :: nil)
  | tl_step: forall c1 c2 lc, non_Sseq c1 -> unfold_Sseq_rel c2 lc ->
                 unfold_Sseq_rel (Ssequence c1 c2) (c1 :: lc)
  | hd_step: forall c1 c2 c3 lc, unfold_Sseq_rel (Ssequence c1 (Ssequence c2 c3)) lc ->
                 unfold_Sseq_rel (Ssequence (Ssequence c1 c2) c3) lc
  .

(* Specifications: *)
Lemma unfold_Sseq_rel_non_nil: forall {c} {P: Prop}, unfold_Sseq_rel c nil -> P.