Fixpoint size_stmt (s: stmt) : nat :=
  match s with
  | Sskip => 0
  | Sseq s1 s2 => (size_stmt s1 + size_stmt s2 + 1)
  | Sifthenelse c s1 s2 => (size_stmt s1 + size_stmt s2 + 1)
  | Sloop s1 => (size_stmt s1 + 1)
  | Sblock s1 => (size_stmt s1 + 1)
  | Sexit n => 0
  | Slabel lbl s1 => (size_stmt s1 + 1)
  | _ => 1
  end.Fixpoint size_cont (k: cont) : nat :=
  match k with
  | Kseq s k1 => (size_stmt s + size_cont k1 + 1)
  | Kblock k1 => (size_cont k1 + 1)
  | _ => 0%nat
  end.Definition measure_state (S: CMinSel_core) :=
  match S with
  | CMinSel_State _ s k _ _ => (size_stmt s + size_cont k, size_stmt s)
  | _                           => (0, 0)
  end.Definition lt_state (S1 S2: CMinSel_core) :=
  lex_ord lt lt (measure_state S1) (measure_state S2).

(* Specifications: *)
Lemma lt_state_intro: forall f1 s1 k1 sp1 e1 f2 s2 k2 sp2 e2, size_stmt s1 + size_cont k1 < size_stmt s2 + size_cont k2 \/ (size_stmt s1 + size_cont k1 = size_stmt s2 + size_cont k2 /\ size_stmt s1 < size_stmt s2) -> lt_state (CMinSel_State f1 s1 k1 sp1 e1) (CMinSel_State f2 s2 k2 sp2 e2).