(*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_incr2: forall mu j FreshS FreshT
(INC : inject_incr (as_inj mu) j) mu'
(Heqmu' : mu' = sm_add_intern mu j FreshS FreshT),
inject_incr j (as_inj mu').