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_initial: forall v1 v2 sig entrypoints (EP: In (v1, v2, sig) entrypoints) (entry_points_ok : forall (v1 v2 : val) (sig : signature), In (v1, v2, sig) entrypoints -> exists b f1 f2, v1 = Vptr b Int.zero /\ v2 = Vptr b Int.zero /\ Genv.find_funct_ptr ge b = Some f1 /\ Genv.find_funct_ptr tge b = Some f2) vals1 c1 m1 j vals2 m2 (DomS DomT : block -> bool) (Ini: initial_core cminsel_eff_sem ge v1 vals1 = Some c1) (Inj: Mem.inject j m1 m2) (VInj: Forall2 (val_inject j) vals1 vals2) (PG:meminj_preserves_globals ge j) (R : list_norepet (map fst (prog_defs prog))) (J: forall b1 b2 delta, j b1 = Some (b2, delta) -> (DomS b1 = true /\ DomT b2 = true)) (RCH: forall b, REACH m2 (fun b' : block => isGlobalBlock tge b' || getBlocks vals2 b') b = true -> DomT b = true) (InitMem : exists m0 : mem, Genv.init_mem prog = Some m0 /\ Ple (Mem.nextblock m0) (Mem.nextblock m1) /\ Ple (Mem.nextblock m0) (Mem.nextblock m2)) (GDE: genvs_domain_eq ge tge) (HDomS: forall b : block, DomS b = true -> Mem.valid_block m1 b) (HDomT: forall b : block, DomT b = true -> Mem.valid_block m2 b), exists c2, initial_core rtl_eff_sem tge v2 vals2 = Some c2 /\ MATCH c1 (initial_SM DomS DomT (REACH m1 (fun b : block => isGlobalBlock ge b || getBlocks vals1 b)) (REACH m2 (fun b : block => isGlobalBlock tge b || getBlocks vals2 b)) j) c1 m1 c2 m2.