(*FreshS/T: fresh blocks in src/tgt language*)
Definition sm_add_intern (mu: SM_Injection) j FreshS FreshT : SM_Injection :=
  Build_SM_Injection (fun b => locBlocksSrc mu b || FreshS b)
                     (fun b => locBlocksTgt mu b || FreshT b)
                     (pubBlocksSrc mu) (pubBlocksTgt mu)
                     (join (local_of mu) (fun b => match extern_of mu b with
                                             None => j b | Some _ => None end))
                     (extBlocksSrc mu) (extBlocksTgt mu)
                     (frgnBlocksSrc mu) (frgnBlocksTgt mu) (extern_of mu).

Lemma Match_eff_diagram_strong_perm: forall (GDE : genvs_domain_eq ge tge) st1 m1 st1' m1' (U1 : block -> Z -> bool) (CS: effstep cmin_eff_sem ge U1 st1 m1 st1' m1') st2 mu m2 (EffSrc: forall b ofs, U1 b ofs = true -> Mem.valid_block m1 b -> vis mu b = true) (MC: Match_cores st1 mu st1 m1 st2 m2) (R: list_norepet (map fst (prog_defs prog))), exists st2' m2' (U2 : block -> Z -> bool), (effstep_plus cminsel_eff_sem tge U2 st2 m2 st2' m2' \/ (measure st1' < measure st1)%nat /\ effstep_star cminsel_eff_sem tge U2 st2 m2 st2' m2') /\ exists mu', intern_incr mu mu' /\ sm_inject_separated mu mu' m1 m2 /\ sm_locally_allocated mu mu' m1 m2 m1' m2' /\ Match_cores st1' mu' st1' m1' st2' m2' /\ SM_wd mu' /\ sm_valid mu' m1' m2' /\ (forall b2 ofs, U2 b2 ofs = true -> Mem.valid_block m2 b2 /\ (locBlocksTgt mu b2 = false -> exists (b1 : block) (delta1 : Z), foreign_of mu b1 = Some (b2, delta1) /\ U1 b1 (ofs - delta1) = true /\ Mem.perm m1 b1 (ofs - delta1) Max Nonempty)).