Definition extern_incr (mu mu': SM_Injection): Prop :=
   inject_incr (extern_of mu) (extern_of mu') /\
   (local_of mu = local_of mu') /\
   (forall b, extBlocksSrc mu b = true -> extBlocksSrc mu' b = true) /\
   (forall b, extBlocksTgt mu b = true -> extBlocksTgt mu' b = true) /\
   (locBlocksSrc mu = locBlocksSrc mu') /\
   (locBlocksTgt mu = locBlocksTgt mu') /\
   (pubBlocksSrc mu = pubBlocksSrc mu') /\
   (pubBlocksTgt mu = pubBlocksTgt mu') /\
   (frgnBlocksSrc mu = frgnBlocksSrc mu') /\
   (frgnBlocksTgt mu = frgnBlocksTgt mu').

Lemma extern_incr_priv: forall mu mu' (INC: extern_incr mu mu'), priv_of mu = priv_of mu'.