(*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_corestep: forall (GDE : genvs_domain_eq ge tge)
st1 m1 st1' m1' (CS: corestep cmin_eff_sem ge st1 m1 st1' m1')
st2 mu m2 (MC: Match_cores st1 mu st1 m1 st2 m2)
(R: list_norepet (map fst (prog_defs prog))),
exists st2' m2',
(corestep_plus cminsel_eff_sem tge st2 m2 st2' m2' \/
(measure st1' < measure st1)%nat /\
corestep_star cminsel_eff_sem tge 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'.