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 MATCH_corestep: forall (*(FE : Clight.function -> list val -> mem -> Clight.env -> Clight.temp_env -> mem -> Prop) (FE_FWD : forall f vargs m e lenv m', FE f vargs m e lenv m' -> mem_forward m m') (FE_UNCH : forall f vargs m e lenv m', FE f vargs m e lenv m' ->( Mem.unchanged_on (fun b z => EmptyEffect b z = false) m m'))*) (GDE : genvs_domain_eq ge tge) (st1 : CL_core) (m1 : mem) (st1' : CL_core) (m1' : mem) (* (CS: corestep (clight_eff_sem FE FE_FWD FE_UNCH) ge st1 m1 st1' m1')*) (CS: corestep CL_eff_sem2 ge st1 m1 st1' m1') (st2 : CSharpMin_core) (mu : SM_Injection) (m2 : mem) (MC: MATCH st1 mu st1 m1 st2 m2), exists (st2' : CSharpMin_core) (m2' : mem) (mu' : SM_Injection), corestep_plus csharpmin_eff_sem tge st2 m2 st2' m2' /\ intern_incr mu mu' /\ sm_inject_separated mu mu' m1 m2 /\ sm_locally_allocated mu mu' m1 m2 m1' m2' /\ MATCH st1' mu' st1' m1' st2' m2' /\ SM_wd mu' /\ sm_valid mu' m1' m2'.