(*DOM/RNG: all blocks mentioned by a SM_Injection. Used for
  stating match_validblocks etc*)
Definition DomSrc (mu: SM_Injection) (b1: block): bool :=
     locBlocksSrc mu b1 || extBlocksSrc mu b1.Definition DOM (mu: SM_Injection) (b1: block): Prop := DomSrc mu b1 = true.Definition DomTgt (mu: SM_Injection) (b2: block): bool :=
     locBlocksTgt mu b2 || extBlocksTgt mu b2.Definition RNG (mu: SM_Injection) (b2:block): Prop := DomTgt mu b2 = true.(*we enforce
  pub_of mu = pub_of mu', via
  pubBlocksSrc/Tgt mu = pubBlocksSrc/Tgt mu':
  it suffices to reclassify leakage at at/afterExternal.
  This enables the proof of
  effect_corediagram_trans.diagram_injinj etc*)
Definition intern_incr (mu mu': SM_Injection): Prop :=
   inject_incr (local_of mu) (local_of mu') /\
   (extern_of mu = extern_of mu') /\
   (forall b, locBlocksSrc mu b = true -> locBlocksSrc mu' b = true) /\
   (forall b, locBlocksTgt mu b = true -> locBlocksTgt mu' b = true) /\
   (pubBlocksSrc mu = pubBlocksSrc mu') /\
   (pubBlocksTgt mu = pubBlocksTgt mu') /\
   (frgnBlocksSrc mu = frgnBlocksSrc mu') /\
   (frgnBlocksTgt mu = frgnBlocksTgt mu') /\
   (extBlocksSrc mu = extBlocksSrc mu') /\
   (extBlocksTgt mu = extBlocksTgt mu').

Lemma intern_incr_foreign: forall mu mu' (INC: intern_incr mu mu'), foreign_of mu = foreign_of mu'.