Program Definition rel_expr {CS: compspecs} (e: expr) (v: val) (rho: environ) : pred rmap :=
    fun phi => rel_expr' rho phi e v.Program Definition rel_lvalue {CS: compspecs}  (e: expr) (v: val) (rho: environ) : pred rmap :=
    fun phi => rel_lvalue' rho phi e v.Definition rel_lvalue'_expr'_sch CS rho phi P P0 :=
  fun H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 H11 H12 H13 H14 H15 H16 H17 =>
  conj (rel_expr'_sch CS rho phi P P0 H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 H11 H12 H13 H14 H15 H16 H17)
       (rel_lvalue'_sch CS rho phi P P0 H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 H11 H12 H13 H14 H15 H16 H17).

Lemma rel_LR_extend: forall {CS: compspecs} e v rho w, (rel_expr' rho w e v -> forall w', extendM w w' -> rel_expr' rho w' e v) /\ (rel_lvalue' rho w e v -> forall w', extendM w w' -> rel_lvalue' rho w' e v).