Definition MATCH (d:CL_core) mu c1 m1 c2 m2:Prop :=
  match_states (restrict (as_inj mu) (vis mu)) c1 m1 c2 m2 /\
  REACH_closed m1 (vis mu) /\
  meminj_preserves_globals ge (as_inj mu) /\
  globalfunction_ptr_inject (as_inj mu) /\
  (forall b, isGlobalBlock ge b = true -> frgnBlocksSrc mu b = true) /\
  sm_valid mu m1 m2 /\ SM_wd mu /\ Mem.inject (as_inj mu) m1 m2.

Lemma transl_expr_correctMu: forall e le m a v te tle tm mu (EVAL: Clight.eval_expr ge e le m a v) (MENV : match_env (restrict (as_inj mu) (vis mu)) e te) (TENV : match_tempenv (restrict (as_inj mu) (vis mu)) le tle) (INJ : Mem.inject (as_inj mu) m tm) (PG : meminj_preserves_globals ge (as_inj mu)) (RC: REACH_closed m (vis mu)) (GLOB: forall b, isGlobalBlock ge b = true -> frgnBlocksSrc mu b = true), forall ta, transl_expr a = OK ta -> exists tv, val_inject (restrict (as_inj mu) (vis mu)) v tv /\ eval_expr tge te tle tm ta tv.