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_DOM:
forall mu mu' (Inc: extern_incr mu mu') b,
DOM mu b -> DOM mu' b.