(*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').

(* Specifications: *)
Lemma intern_incr_locBlocksSrc mu mu':
intern_incr mu mu' -> forall b,
locBlocksSrc mu b = true -> locBlocksSrc mu' b = true.
Lemma intern_incr_DOM:
forall mu mu' (Inc: intern_incr mu mu') b,
DOM mu b -> DOM mu' b.
Lemma intern_incr_RNG:
forall mu mu' (Inc: intern_incr mu mu') b,
RNG mu b -> RNG mu' b.
Lemma intern_incr_DomTgt_inv: forall mu mu' (INC: intern_incr mu mu') b,
DomTgt mu' b = false -> DomTgt mu b = false.
Lemma intern_incr_locBlocksSrc_inv: forall mu mu' (INC: intern_incr mu mu') b,
locBlocksSrc mu' b = false -> locBlocksSrc mu b = false.
Lemma intern_incr_locBlocksTgt_inv: forall mu mu' (INC: intern_incr mu mu') b,
locBlocksTgt mu' b = false -> locBlocksTgt mu b = false.
Lemma intern_incr_priv: forall mu mu' (INC: intern_incr mu mu'),
inject_incr (priv_of mu) (priv_of mu').
Lemma intern_incr_pub: forall mu mu' (INC: intern_incr mu mu')
(WD: SM_wd mu), pub_of mu = pub_of mu'.
Lemma intern_incr_foreign: forall mu mu' (INC: intern_incr mu mu'),
foreign_of mu = foreign_of mu'.
Lemma intern_incr_unknown: forall mu mu' (INC: intern_incr mu mu')
(WD': SM_wd mu'), unknown_of mu = unknown_of mu'.
Lemma intern_incr_DomSrc:
forall mu mu' (Inc: intern_incr mu mu') b,
DomSrc mu b = true -> DomSrc mu' b = true.
Lemma intern_incr_DOM:
forall mu mu' (Inc: intern_incr mu mu') b,
DOM mu b -> DOM mu' b.
Lemma intern_incr_RNG:
forall mu mu' (Inc: intern_incr mu mu') b,
RNG mu b -> RNG mu' b.
Lemma intern_incr_DomTgt_inv: forall mu mu' (INC: intern_incr mu mu') b,
DomTgt mu' b = false -> DomTgt mu b = false.
Lemma intern_incr_locBlocksSrc_inv: forall mu mu' (INC: intern_incr mu mu') b,
locBlocksSrc mu' b = false -> locBlocksSrc mu b = false.
Lemma intern_incr_locBlocksTgt_inv: forall mu mu' (INC: intern_incr mu mu') b,
locBlocksTgt mu' b = false -> locBlocksTgt mu b = false.
Lemma intern_incr_priv: forall mu mu' (INC: intern_incr mu mu'),
inject_incr (priv_of mu) (priv_of mu').
Lemma intern_incr_pub: forall mu mu' (INC: intern_incr mu mu')
(WD: SM_wd mu), pub_of mu = pub_of mu'.
Lemma intern_incr_foreign: forall mu mu' (INC: intern_incr mu mu'),
foreign_of mu = foreign_of mu'.
Lemma intern_incr_unknown: forall mu mu' (INC: intern_incr mu mu')
(WD': SM_wd mu'), unknown_of mu = unknown_of mu'.