Step
*
1
1
of Lemma
pi-rep-trans_wf
.....subterm..... T:t
1:n
1. l_loc : Id
2. P : pi_term()
3. g : {Q:pi_term()| pi-rank(Q) < pi-rank(pirep(P))} ─→ Id ─→ Name ─→ (Name List) ─→ pi-process()
4. l : Id@i
5. serial : Name@i
6. avoid : Name List@i
⊢ RecProcess(0;s,m.if (s =z 0) ∧b pDVfire?(m) then <1, make-lg([<l_loc, mk-tagged("msg";pDVloc(l))>])>
if (s =z 1) ∧b pDVloc_tag?(m)
then let l1 = pDVloc_tag-id(m) in
let n1 = pDVloc_tag-name(m) in
<0, lg-add(make-lg([<l1, mk-tagged("create";g P l1 n1 avoid)>; <l1, mk-tagged("msg";pDVfire())>; <l, mk-tagged\000C("msg";pDVfire())>]);0;1)>
else <s, make-lg([])>
fi ) ∈ pi-process()
BY
{ (Using [`S',⌈ℕ4⌉] (BLemma `rec-process_wf_pi_simple_state`)⋅ THENA Try (Complete (Auto)))⋅ }
1
.....wf.....
1. l_loc : Id
2. P : pi_term()
3. g : {Q:pi_term()| pi-rank(Q) < pi-rank(pirep(P))} ─→ Id ─→ Name ─→ (Name List) ─→ pi-process()
4. l : Id@i
5. serial : Name@i
6. avoid : Name List@i
⊢ λs,m. if (s =z 0) ∧b pDVfire?(m) then <1, make-lg([<l_loc, mk-tagged("msg";pDVloc(l))>])>
if (s =z 1) ∧b pDVloc_tag?(m)
then let l1 = pDVloc_tag-id(m) in
let n1 = pDVloc_tag-name(m) in
<0, lg-add(make-lg([<l1, mk-tagged("create";g P l1 n1 avoid)>; <l1, mk-tagged("msg";pDVfire())>; <l, mk-t\000Cagged("msg";pDVfire())>]);0;1)>
else <s, make-lg([])>
fi ∈ ∩T:{T:Type| pi-process() ⊆r T} . (ℕ4 ─→ piM(T) ─→ (ℕ4 × LabeledDAG(Id × (Com(T.piM(T)) T))))
Latex:
Latex:
.....subterm..... T:t
1:n
1. l$_{loc}$ : Id
2. P : pi\_term()
3. g : \{Q:pi\_term()| pi-rank(Q) < pi-rank(pirep(P))\} {}\mrightarrow{} Id {}\mrightarrow{} Name {}\mrightarrow{} (Name List) {}\mrightarrow{} pi-process()
4. l : Id@i
5. serial : Name@i
6. avoid : Name List@i
\mvdash{} RecProcess(0;s,m.if (s =\msubz{} 0) \mwedge{}\msubb{} pDVfire?(m) then ə, make-lg([<l$_{loc}$, mk-t\000Cagged("msg";pDVloc(l))>])>
if (s =\msubz{} 1) \mwedge{}\msubb{} pDVloc\_tag?(m)
then let l1 = pDVloc\_tag-id(m) in
let n1 = pDVloc\_tag-name(m) in
ɘ
, lg-add(make-lg([<l1, mk-tagged("create";g P l1 n1 avoid)>
<l1, mk-tagged("msg";pDVfire())>
<l, mk-tagged("msg";pDVfire())>]);0;1)
>
else <s, make-lg([])>
fi ) \mmember{} pi-process()
By
Latex:
(Using [`S',\mkleeneopen{}\mBbbN{}4\mkleeneclose{}] (BLemma `rec-process\_wf\_pi\_simple\_state`)\mcdot{} THENA Try (Complete (Auto)))\mcdot{}
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