Definition MATCH (d:CMinSel_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_effcore_diagram: forall st1 m1 st1' m1' (U1 : block -> Z -> bool) (CS: effstep cminsel_eff_sem ge U1 st1 m1 st1' m1') st2 mu m2 (UHyp: forall b z, U1 b z = true -> Mem.valid_block m1 b -> vis mu b = true) (MTCH: MATCH st1 mu st1 m1 st2 m2), exists st2' m2' mu', exists U2 : block -> Z -> bool, (effstep_plus rtl_eff_sem tge U2 st2 m2 st2' m2' \/ effstep_star rtl_eff_sem tge U2 st2 m2 st2' m2' /\ lt_state st1' st1) /\ 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' /\ (forall (b : block) (ofs : Z), U2 b ofs = true -> Mem.valid_block m2 b /\ (locBlocksTgt mu b = false -> exists (b1 : block) (delta1 : Z), foreign_of mu b1 = Some (b, delta1) /\ U1 b1 (ofs - delta1)%Z = true /\ Mem.perm m1 b1 (ofs - delta1) Max Nonempty)).