Proof of Nuprl Lemma : pv11_p1_commander_state_from

Step * 1 of Lemma pv11_p1_commander_state_from_p2bs

1. Cmd : {T:Type| valueall-type(T)} @i'
2. f : pv11_p1_headers_type{i:l}(Cmd)@i'
3. (f [decision]) = (ℤ × Cmd) ∈ Type
4. (f [propose]) = (ℤ × Cmd) ∈ Type

5. (f ``pv11_p1 adopted``) = (pv11_p1_Ballot_Num() × ((pv11_p1_Ballot_Num() × ℤ × Cmd) List)) ∈ Type

6. (f ``pv11_p1 preempted``) = pv11_p1_Ballot_Num() ∈ Type
7. (f ``pv11_p1 p2b``) = (Id × pv11_p1_Ballot_Num() × ℤ × pv11_p1_Ballot_Num()) ∈ Type
8. (f ``pv11_p1 p2a``) = (Id × pv11_p1_Ballot_Num() × ℤ × Cmd) ∈ Type
9. (f ``pv11_p1 p1b``)
= (Id × pv11_p1_Ballot_Num() × pv11_p1_Ballot_Num() × ((pv11_p1_Ballot_Num() × ℤ × Cmd) List))
∈ Type
10. (f ``pv11_p1 p1a``) = (Id × pv11_p1_Ballot_Num()) ∈ Type
11. f ∈ Name ─→ Type
12. es : EO+(Message(f))@i'
13. start : E@i
14. e : E@i
15. e0 : E@i
16. accpts : bag(Id)@i
17. ldrs : bag(Id)@i
18. ldrs_uid : Id ─→ ℤ@i
19. reps : bag(Id)@i
20. b : pv11_p1_Ballot_Num()@i
21. s : ℤ@i
22. c : Cmd@i
23. waitfor : bag(Id)@i
24. i : Id@i
25. l : Id@i
26. start ≤loc e @i
27. Inj(Id;ℤ;ldrs_uid)@i
28. pv11_p1_message-constraint{paxos-v11-part1.esh:o}(Cmd; accpts; ldrs; ldrs_uid; reps; f; es)@i
29. pv11_p1_p2a'send(Cmd;f) i <l, b, s, c> ∈ pv11_p1_main(Cmd;accpts;ldrs;ldrs_uid;reps;f)(e0)@i
30. waitfor = pv11_p1_CommanderStateFun(Cmd;accpts;f;b;s;es.start;e) ∈ bag(Id)@i
⊢ ↓∃L:E List
    ((waitfor = [i∈accpts|¬_bi ∈_b map(λe.loc(e);L))] ∈ bag(Id))
    ∧ (∀e':E
         ((e' ∈ L)
         ⇒ ((e' < e)
            ∧ loc(e') ↓∈ accpts
            ∧ (b = (fst(pv11_p1_AcceptorStateFun(Cmd;ldrs_uid;f;es;e'))) ∈ pv11_p1_Ballot_Num())
            ∧ (<b, s, c> ∈ snd(pv11_p1_AcceptorStateFun(Cmd;ldrs_uid;f;es;e')))))))
BY
{ (RepeatFor 2 (MoveToConcl (-1))
   THEN RepeatFor 6 (MoveToConcl (-3))
   THEN RepeatFor 2 (MoveToConcl (-8))
   THEN CausalInd'
   THEN Auto
   THEN MoveToConcl (-1)
   THEN (RWO "pv11_p1_commander_state_fun_eq" 0 THENA Auto)
   THEN (Subst ⌈e ∈_b pv11_p1_p2b'base(Cmd;f) ~ e ∈_b pv11_p1_p2b'base(Cmd;f)⌉ 0⋅
         THENA (RepUR ``pv11_p1_p2b'base`` 0 THEN BLemma `eo-forward-member-eclass` THEN Auto)
         )
   THEN Repeat (AutoSplit)
   THEN Try ((Assert ⌈header(e) = ``pv11_p1 p2b`` ∈ Name⌉⋅

              THENA OnSomeHyp(\i.(RepUR ``pv11_p1_p2b'base`` i THEN FLemma `member-base-class` [i] THEN CpltAuto))⋅

              ))
   THEN Try ((Subst ⌈pv11_p1_p2b'base(Cmd;f)@e ~ pv11_p1_p2b'base(Cmd;f)@e⌉ 0⋅
              THENA (RepUR ``pv11_p1_p2b'base`` 0

                     THEN Using [`T',⌈Id × pv11_p1_Ballot_Num() × ℤ × pv11_p1_Ballot_Num()⌉

                     ] (BLemma `eo-forward-base-classfun-res-sq`)⋅
                     THEN CpltAuto)
              ))
   THEN Try ((RepUR ``pv11_p1_p2b'base`` 0 THEN RWO "classfun-res-base" 0 THEN Try (CpltAuto)))

   THEN Try ((Assert ⌈has-es-info-type(es;e;f;Id × pv11_p1_Ballot_Num() × ℤ × pv11_p1_Ballot_Num())⌉⋅

THENA CpltAuto
))) }

1
1. Cmd : {T:Type| valueall-type(T)} @i'
2. f : pv11_p1_headers_type{i:l}(Cmd)@i'
3. (f [decision]) = (ℤ × Cmd) ∈ Type
4. (f [propose]) = (ℤ × Cmd) ∈ Type

5. (f ``pv11_p1 adopted``) = (pv11_p1_Ballot_Num() × ((pv11_p1_Ballot_Num() × ℤ × Cmd) List)) ∈ Type

                          ∧ (b = (fst(pv11_p1_AcceptorStateFun(Cmd;ldrs_uid;f;es;e'))) ∈ pv11_p1_Ballot_Num())

                          ∧ (<b, s, c> ∈ snd(pv11_p1_AcceptorStateFun(Cmd;ldrs_uid;f;es;e')))))))))))

23. e0 : E@i
24. s : ℤ@i
25. c : Cmd@i
26. waitfor : bag(Id)@i
27. i : Id@i
28. l : Id@i
29. start ≤loc e @i
30. pv11_p1_p2a'send(Cmd;f) i <l, b, s, c> ∈ pv11_p1_main(Cmd;accpts;ldrs;ldrs_uid;reps;f)(e0)@i
31. ↑e ∈_b pv11_p1_p2b'base(Cmd;f)
32. ↑first(e)
33. header(e) = ``pv11_p1 p2b`` ∈ Name
34. has-es-info-type(es;e;f;Id × pv11_p1_Ballot_Num() × ℤ × pv11_p1_Ballot_Num())
⊢ (waitfor = (pv11_p1_on_p2b() b s loc(e) msgval(e) accpts) ∈ bag(Id))
⇒ (↓∃L:E List
      ((waitfor = [i∈accpts|¬_bi ∈_b map(λe.loc(e);L))] ∈ bag(Id))
      ∧ (∀e':E
           ((e' ∈ L)
           ⇒ ((e' < e)
              ∧ loc(e') ↓∈ accpts

              ∧ (b = (fst(pv11_p1_AcceptorStateFun(Cmd;ldrs_uid;f;es;e'))) ∈ pv11_p1_Ballot_Num())

∧ (<b, s, c> ∈ snd(pv11_p1_AcceptorStateFun(Cmd;ldrs_uid;f;es;e'))))))))

2
1. Cmd : {T:Type| valueall-type(T)} @i'
2. f : pv11_p1_headers_type{i:l}(Cmd)@i'
3. (f [decision]) = (ℤ × Cmd) ∈ Type
4. (f [propose]) = (ℤ × Cmd) ∈ Type

5. (f ``pv11_p1 adopted``) = (pv11_p1_Ballot_Num() × ((pv11_p1_Ballot_Num() × ℤ × Cmd) List)) ∈ Type

6. (f ``pv11_p1 preempted``) = pv11_p1_Ballot_Num() ∈ Type
7. (f ``pv11_p1 p2b``) = (Id × pv11_p1_Ballot_Num() × ℤ × pv11_p1_Ballot_Num()) ∈ Type
8. (f ``pv11_p1 p2a``) = (Id × pv11_p1_Ballot_Num() × ℤ × Cmd) ∈ Type
9. (f ``pv11_p1 p1b``)
= (Id × pv11_p1_Ballot_Num() × pv11_p1_Ballot_Num() × ((pv11_p1_Ballot_Num() × ℤ × Cmd) List))
∈ Type
10. (f ``pv11_p1 p1a``) = (Id × pv11_p1_Ballot_Num()) ∈ Type
11. f ∈ Name ─→ Type
12. es : EO+(Message(f))@i'
13. start : E@i
14. accpts : bag(Id)@i
15. ldrs : bag(Id)@i
16. ldrs_uid : Id ─→ ℤ@i
17. reps : bag(Id)@i
18. b : pv11_p1_Ballot_Num()@i
19. Inj(Id;ℤ;ldrs_uid)@i
20. pv11_p1_message-constraint{paxos-v11-part1.esh:o}(Cmd; accpts; ldrs; ldrs_uid; reps; f; es)@i
21. e : E@i
22. ¬↑first(e)
23. ∀e1:E
      ((e1 < e)
      ⇒ (∀e0:E. ∀s:ℤ. ∀c:Cmd. ∀waitfor:bag(Id). ∀i,l:Id.
            (start ≤loc e1
            ⇒ pv11_p1_p2a'send(Cmd;f) i <l, b, s, c> ∈ pv11_p1_main(Cmd;accpts;ldrs;ldrs_uid;reps;f)(e0)
            ⇒ (waitfor = pv11_p1_CommanderStateFun(Cmd;accpts;f;b;s;es.start;e1) ∈ bag(Id))
            ⇒ (↓∃L:E List
                  ((waitfor = [i∈accpts|¬_bi ∈_b map(λe.loc(e);L))] ∈ bag(Id))
                  ∧ (∀e':E
                       ((e' ∈ L)
                       ⇒ ((e' < e1)
                          ∧ loc(e') ↓∈ accpts

                          ∧ (b = (fst(pv11_p1_AcceptorStateFun(Cmd;ldrs_uid;f;es;e'))) ∈ pv11_p1_Ballot_Num())

                          ∧ (<b, s, c> ∈ snd(pv11_p1_AcceptorStateFun(Cmd;ldrs_uid;f;es;e')))))))))))

24. e0 : E@i
25. s : ℤ@i
26. c : Cmd@i
27. waitfor : bag(Id)@i
28. i : Id@i
29. l : Id@i
30. start ≤loc e @i
31. pv11_p1_p2a'send(Cmd;f) i <l, b, s, c> ∈ pv11_p1_main(Cmd;accpts;ldrs;ldrs_uid;reps;f)(e0)@i
32. ↑e ∈_b pv11_p1_p2b'base(Cmd;f)
33. header(e) = ``pv11_p1 p2b`` ∈ Name
34. has-es-info-type(es;e;f;Id × pv11_p1_Ballot_Num() × ℤ × pv11_p1_Ballot_Num())
⊢ (waitfor
= (pv11_p1_on_p2b() b s loc(e) msgval(e) pv11_p1_CommanderStateFun(Cmd;accpts;f;b;s;es.start;pred(e)))
∈ bag(Id))
⇒ (↓∃L:E List
      ((waitfor = [i∈accpts|¬_bi ∈_b map(λe.loc(e);L))] ∈ bag(Id))
      ∧ (∀e':E
           ((e' ∈ L)
           ⇒ ((e' < e)
              ∧ loc(e') ↓∈ accpts

              ∧ (b = (fst(pv11_p1_AcceptorStateFun(Cmd;ldrs_uid;f;es;e'))) ∈ pv11_p1_Ballot_Num())

∧ (<b, s, c> ∈ snd(pv11_p1_AcceptorStateFun(Cmd;ldrs_uid;f;es;e'))))))))

3
1. Cmd : {T:Type| valueall-type(T)} @i'
2. f : pv11_p1_headers_type{i:l}(Cmd)@i'
3. (f [decision]) = (ℤ × Cmd) ∈ Type
4. (f [propose]) = (ℤ × Cmd) ∈ Type

5. (f ``pv11_p1 adopted``) = (pv11_p1_Ballot_Num() × ((pv11_p1_Ballot_Num() × ℤ × Cmd) List)) ∈ Type

6. (f ``pv11_p1 preempted``) = pv11_p1_Ballot_Num() ∈ Type
7. (f ``pv11_p1 p2b``) = (Id × pv11_p1_Ballot_Num() × ℤ × pv11_p1_Ballot_Num()) ∈ Type
8. (f ``pv11_p1 p2a``) = (Id × pv11_p1_Ballot_Num() × ℤ × Cmd) ∈ Type
9. (f ``pv11_p1 p1b``)
= (Id × pv11_p1_Ballot_Num() × pv11_p1_Ballot_Num() × ((pv11_p1_Ballot_Num() × ℤ × Cmd) List))
∈ Type
10. (f ``pv11_p1 p1a``) = (Id × pv11_p1_Ballot_Num()) ∈ Type
11. f ∈ Name ─→ Type
12. es : EO+(Message(f))@i'
13. start : E@i
14. accpts : bag(Id)@i
15. ldrs : bag(Id)@i
16. ldrs_uid : Id ─→ ℤ@i
17. reps : bag(Id)@i
18. b : pv11_p1_Ballot_Num()@i
19. Inj(Id;ℤ;ldrs_uid)@i
20. pv11_p1_message-constraint{paxos-v11-part1.esh:o}(Cmd; accpts; ldrs; ldrs_uid; reps; f; es)@i
21. e : E@i
22. ¬↑e ∈_b pv11_p1_p2b'base(Cmd;f)
23. ∀e1:E
      ((e1 < e)
      ⇒ (∀e0:E. ∀s:ℤ. ∀c:Cmd. ∀waitfor:bag(Id). ∀i,l:Id.
            (start ≤loc e1
            ⇒ pv11_p1_p2a'send(Cmd;f) i <l, b, s, c> ∈ pv11_p1_main(Cmd;accpts;ldrs;ldrs_uid;reps;f)(e0)
            ⇒ (waitfor = pv11_p1_CommanderStateFun(Cmd;accpts;f;b;s;es.start;e1) ∈ bag(Id))
            ⇒ (↓∃L:E List
                  ((waitfor = [i∈accpts|¬_bi ∈_b map(λe.loc(e);L))] ∈ bag(Id))
                  ∧ (∀e':E
                       ((e' ∈ L)
                       ⇒ ((e' < e1)
                          ∧ loc(e') ↓∈ accpts

                          ∧ (b = (fst(pv11_p1_AcceptorStateFun(Cmd;ldrs_uid;f;es;e'))) ∈ pv11_p1_Ballot_Num())

                          ∧ (<b, s, c> ∈ snd(pv11_p1_AcceptorStateFun(Cmd;ldrs_uid;f;es;e')))))))))))

24. e0 : E@i
25. s : ℤ@i
26. c : Cmd@i
27. waitfor : bag(Id)@i
28. i : Id@i
29. l : Id@i
30. start ≤loc e @i
31. pv11_p1_p2a'send(Cmd;f) i <l, b, s, c> ∈ pv11_p1_main(Cmd;accpts;ldrs;ldrs_uid;reps;f)(e0)@i
32. ↑first(e)
⊢ (waitfor = accpts ∈ bag(Id))
⇒ (↓∃L:E List
      ((waitfor = [i∈accpts|¬_bi ∈_b map(λe.loc(e);L))] ∈ bag(Id))
      ∧ (∀e':E
           ((e' ∈ L)
           ⇒ ((e' < e)
              ∧ loc(e') ↓∈ accpts

              ∧ (b = (fst(pv11_p1_AcceptorStateFun(Cmd;ldrs_uid;f;es;e'))) ∈ pv11_p1_Ballot_Num())

∧ (<b, s, c> ∈ snd(pv11_p1_AcceptorStateFun(Cmd;ldrs_uid;f;es;e'))))))))

4
1. Cmd : {T:Type| valueall-type(T)} @i'
2. f : pv11_p1_headers_type{i:l}(Cmd)@i'
3. (f [decision]) = (ℤ × Cmd) ∈ Type
4. (f [propose]) = (ℤ × Cmd) ∈ Type

5. (f ``pv11_p1 adopted``) = (pv11_p1_Ballot_Num() × ((pv11_p1_Ballot_Num() × ℤ × Cmd) List)) ∈ Type

6. (f ``pv11_p1 preempted``) = pv11_p1_Ballot_Num() ∈ Type
7. (f ``pv11_p1 p2b``) = (Id × pv11_p1_Ballot_Num() × ℤ × pv11_p1_Ballot_Num()) ∈ Type
8. (f ``pv11_p1 p2a``) = (Id × pv11_p1_Ballot_Num() × ℤ × Cmd) ∈ Type
9. (f ``pv11_p1 p1b``)
= (Id × pv11_p1_Ballot_Num() × pv11_p1_Ballot_Num() × ((pv11_p1_Ballot_Num() × ℤ × Cmd) List))
∈ Type
10. (f ``pv11_p1 p1a``) = (Id × pv11_p1_Ballot_Num()) ∈ Type
11. f ∈ Name ─→ Type
12. es : EO+(Message(f))@i'
13. start : E@i
14. accpts : bag(Id)@i
15. ldrs : bag(Id)@i
16. ldrs_uid : Id ─→ ℤ@i
17. reps : bag(Id)@i
18. b : pv11_p1_Ballot_Num()@i
19. Inj(Id;ℤ;ldrs_uid)@i
20. pv11_p1_message-constraint{paxos-v11-part1.esh:o}(Cmd; accpts; ldrs; ldrs_uid; reps; f; es)@i
21. e : E@i
22. ¬↑first(e)
23. ¬↑e ∈_b pv11_p1_p2b'base(Cmd;f)
24. ∀e1:E
      ((e1 < e)
      ⇒ (∀e0:E. ∀s:ℤ. ∀c:Cmd. ∀waitfor:bag(Id). ∀i,l:Id.
            (start ≤loc e1
            ⇒ pv11_p1_p2a'send(Cmd;f) i <l, b, s, c> ∈ pv11_p1_main(Cmd;accpts;ldrs;ldrs_uid;reps;f)(e0)
            ⇒ (waitfor = pv11_p1_CommanderStateFun(Cmd;accpts;f;b;s;es.start;e1) ∈ bag(Id))
            ⇒ (↓∃L:E List
                  ((waitfor = [i∈accpts|¬_bi ∈_b map(λe.loc(e);L))] ∈ bag(Id))
                  ∧ (∀e':E
                       ((e' ∈ L)
                       ⇒ ((e' < e1)
                          ∧ loc(e') ↓∈ accpts

                          ∧ (b = (fst(pv11_p1_AcceptorStateFun(Cmd;ldrs_uid;f;es;e'))) ∈ pv11_p1_Ballot_Num())

                          ∧ (<b, s, c> ∈ snd(pv11_p1_AcceptorStateFun(Cmd;ldrs_uid;f;es;e')))))))))))

25. e0 : E@i
26. s : ℤ@i
27. c : Cmd@i
28. waitfor : bag(Id)@i
29. i : Id@i
30. l : Id@i
31. start ≤loc e @i
32. pv11_p1_p2a'send(Cmd;f) i <l, b, s, c> ∈ pv11_p1_main(Cmd;accpts;ldrs;ldrs_uid;reps;f)(e0)@i
⊢ (waitfor = pv11_p1_CommanderStateFun(Cmd;accpts;f;b;s;es.start;pred(e)) ∈ bag(Id))
⇒ (↓∃L:E List
      ((waitfor = [i∈accpts|¬_bi ∈_b map(λe.loc(e);L))] ∈ bag(Id))
      ∧ (∀e':E
           ((e' ∈ L)
           ⇒ ((e' < e)
              ∧ loc(e') ↓∈ accpts

              ∧ (b = (fst(pv11_p1_AcceptorStateFun(Cmd;ldrs_uid;f;es;e'))) ∈ pv11_p1_Ballot_Num())

∧ (<b, s, c> ∈ snd(pv11_p1_AcceptorStateFun(Cmd;ldrs_uid;f;es;e'))))))))

Latex:

Latex:
1. Cmd : \{T:Type| valueall-type(T)\} @i' 2. f : pv11\_p1\_headers\_type\{i:l\}(Cmd)@i' 3. (f [decision]) = (\mBbbZ{} \mtimes{} Cmd) 4. (f [propose]) = (\mBbbZ{} \mtimes{} Cmd) 5. (f ``pv11\_p1 adopted``) = (pv11\_p1\_Ballot\_Num() \mtimes{} ((pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd) List)) 6. (f ``pv11\_p1 preempted``) = pv11\_p1\_Ballot\_Num() 7. (f ``pv11\_p1 p2b``) = (Id \mtimes{} pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} pv11\_p1\_Ballot\_Num()) 8. (f ``pv11\_p1 p2a``) = (Id \mtimes{} pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd) 9. (f ``pv11\_p1 p1b``) = (Id \mtimes{} pv11\_p1\_Ballot\_Num() \mtimes{} pv11\_p1\_Ballot\_Num() \mtimes{} ((pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} Cmd) List)) 10. (f ``pv11\_p1 p1a``) = (Id \mtimes{} pv11\_p1\_Ballot\_Num()) 11. f \mmember{} Name {}\mrightarrow{} Type 12. es : EO+(Message(f))@i' 13. start : E@i 14. e : E@i 15. e0 : E@i 16. accpts : bag(Id)@i 17. ldrs : bag(Id)@i 18. ldrs$_{uid}$ : Id {}\mrightarrow{} \mBbbZ{}@i 19. reps : bag(Id)@i 20. b : pv11\_p1\_Ballot\_Num()@i 21. s : \mBbbZ{}@i 22. c : Cmd@i 23. waitfor : bag(Id)@i 24. i : Id@i 25. l : Id@i 26. start \mleq{}loc e @i 27. Inj(Id;\mBbbZ{};ldrs$_{uid}$)@i 28. pv11\_p1\_message-constraint\{paxos-v11-part1.esh:o\}(Cmd; accpts; ldrs; ldrs$_{uid}\000C$; reps; f; es)@i 29. pv11\_p1\_p2a'send(Cmd;f) i <l, b, s, c> \mmember{} pv11\_p1\_main(Cmd;accpts;ldrs;ldrs$_{uid\mbackslash{}ff7\000Cd$;reps;f)(e0)@i 30. waitfor = pv11\_p1\_CommanderStateFun(Cmd;accpts;f;b;s;es.start;e)@i \mvdash{} \mdownarrow{}\mexists{}L:E List ((waitfor = [i\mmember{}accpts|\mneg{}\msubb{}i \mmember{}\msubb{} map(\mlambda{}e.loc(e);L))]) \mwedge{} (\mforall{}e':E ((e' \mmember{} L) {}\mRightarrow{} ((e' < e) \mwedge{} loc(e') \mdownarrow{}\mmember{} accpts \mwedge{} (b = (fst(pv11\_p1\_AcceptorStateFun(Cmd;ldrs$_{uid}$;f;es;e')))) \mwedge{} (<b, s, c> \mmember{} snd(pv11\_p1\_AcceptorStateFun(Cmd;ldrs$_{uid}$;f;es;e'\000C))))))) By Latex: (RepeatFor 2 (MoveToConcl (-1)) THEN RepeatFor 6 (MoveToConcl (-3)) THEN RepeatFor 2 (MoveToConcl (-8)) THEN CausalInd' THEN Auto THEN MoveToConcl (-1) THEN (RWO "pv11\_p1\_commander\_state\_fun\_eq" 0 THENA Auto) THEN (Subst \mkleeneopen{}e \mmember{}\msubb{} pv11\_p1\_p2b'base(Cmd;f) \msim{} e \mmember{}\msubb{} pv11\_p1\_p2b'base(Cmd;f)\mkleeneclose{} 0\mcdot{} THENA (RepUR ``pv11\_p1\_p2b'base`` 0 THEN BLemma `eo-forward-member-eclass` THEN Auto) ) THEN Repeat (AutoSplit) THEN Try ((Assert \mkleeneopen{}header(e) = ``pv11\_p1 p2b``\mkleeneclose{}\mcdot{} THENA OnSomeHyp(\mbackslash{}i.(RepUR ``pv11\_p1\_p2b'base`` i THEN FLemma `member-base-class` [i] THEN CpltAuto))\mcdot{} )) THEN Try ((Subst \mkleeneopen{}pv11\_p1\_p2b'base(Cmd;f)@e \msim{} pv11\_p1\_p2b'base(Cmd;f)@e\mkleeneclose{} 0\mcdot{} THENA (RepUR ``pv11\_p1\_p2b'base`` 0 THEN Using [`T',\mkleeneopen{}Id \mtimes{} pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} pv11\_p1\_Ballot\_Num()\mkleeneclose{} ] (BLemma `eo-forward-base-classfun-res-sq`)\mcdot{} THEN CpltAuto) )) THEN Try ((RepUR ``pv11\_p1\_p2b'base`` 0 THEN RWO "classfun-res-base" 0 THEN Try (CpltAuto))) THEN Try ((Assert \mkleeneopen{}has-es-info-type(es;e;f;Id \mtimes{} pv11\_p1\_Ballot\_Num() \mtimes{} \mBbbZ{} \mtimes{} pv11\_p1\_Ballot\_Num())\mkleeneclose{}\mcdot{} THENA CpltAuto ))) Home Index