(*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 sm_add_intern_sep: forall mu j FreshS FreshT
(HFreshS: forall b, FreshS b =true -> DomSrc mu b = false)
(HFreshT: forall b, FreshT b =true -> DomTgt mu b = false)
(JDomTgt: forall b1 b2 d, j b1 = Some (b2,d) ->
as_inj mu b1 = Some(b2,d) \/
(FreshS b1 = true /\ FreshT b2 = true))
mu'
(Heqmu' : mu' = sm_add_intern mu j FreshS FreshT)
m1 m2 (WD: SM_wd mu)
(HFreshSm1: forall b, FreshS b =true -> ~Mem.valid_block m1 b)
(HFreshTm2: forall b, FreshT b =true -> ~Mem.valid_block m2 b),
sm_inject_separated mu mu' m1 m2.