Definition simple_side_effect (r: expr) : Prop :=
  match r with
  | Evalof l _ => simple l = true /\ type_is_volatile (typeof l) = true
  | Eseqand r1 r2 _ => simple r1 = true
  | Eseqor r1 r2 _ => simple r1 = true
  | Econdition r1 r2 r3 _ => simple r1 = true
  | Eassign l1 r2 _ => simple l1 = true /\ simple r2 = true
  | Eassignop _ l1 r2 _ _ => simple l1 = true /\ simple r2 = true
  | Epostincr _ l1 _ => simple l1 = true
  | Ecomma r1 r2 _ => simple r1 = true
  | Ecall r1 rl _ => simple r1 = true /\ simplelist rl = true
  | Ebuiltin ef tyargs rl _ => simplelist rl = true
  | Eparen r1 _ _ => simple r1 = true
  | _ => False
  end.Scheme expr_ind2 := Induction for expr Sort Prop
  with exprlist_ind2 := Induction for exprlist Sort Prop.Combined Scheme expr_expr_list_ind from expr_ind2, exprlist_ind2.

(* Specifications: *)
Lemma decompose_expr: (forall a from C, context from RV C -> safe (ExprState f (C a) k e m) -> simple a = true \/ exists C', exists a', a = C' a' /\ simple_side_effect a' /\ leftcontext RV from C') /\(forall rl C, contextlist' C -> safe (ExprState f (C rl) k e m) -> simplelist rl = true \/ exists C', exists a', rl = C' a' /\ simple_side_effect a' /\ leftcontextlist RV C').
Lemma decompose_expr: (forall a from C, context from RV C -> safe (ExprState f (C a) k e m) -> simple a = true \/ exists C', exists a', a = C' a' /\ simple_side_effect a' /\ leftcontext RV from C') /\(forall rl C, contextlist' C -> safe (ExprState f (C rl) k e m) -> simplelist rl = true \/ exists C', exists a', rl = C' a' /\ simple_side_effect a' /\ leftcontextlist RV C').