Step
*
1
1
2
of Lemma
new_23_sig_progress-step8
1. Cmd : {T:Type| valueall-type(T)}
2. eq : EqDecider(Cmd)
3. reps : bag(Id)
4. clients : bag(Id)
5. coeff : {2...}
6. flrs : ℕ
7. propose : Atom List
8. notify : Atom List
9. slots : set-sig{i:l}(ℤ)
10. f : new_23_sig_headers_type{i:l}(Cmd;notify;propose)
11. (f propose) = (ℤ × Cmd) ∈ Type
12. (f notify) = (ℤ × Cmd) ∈ Type
13. (f ``new_23_sig decided``) = (ℤ × Cmd) ∈ Type
14. (f ``new_23_sig retry``) = (ℤ × ℤ × Cmd) ∈ Type
15. (f ``new_23_sig vote``) = (ℤ × ℤ × Cmd × Id) ∈ Type
16. f ∈ Name ─→ Type
17. es : EO+(Message(f))
18. e : E
19. n : ℤ
20. c : Cmd
21. faulty : bag(Id)
22. msgs-interface-delivered-with-omissions(f;es;new_23_sig_main();faulty;flrs;reps)@i
23. bag-no-repeats(Id;reps)@i
24. #(reps) = ((coeff * flrs) + flrs + 1) ∈ ℤ@i
25. loc(e) ↓∈ reps@i
26. ¬loc(e) ↓∈ faulty@i
27. <n, c> ∈ new_23_sig_Proposal(Cmd;notify;propose;f)(e)@i
28. ¬↑(set-sig-member(slots) n new_23_sig_ReplicaStateFun(Cmd;notify;propose;slots;f;es;e))@i
29. bs : (Id × E × Cmd) List
30. bag-map(λi.(fst(i));bs) = [x∈reps|¬bbag-deq-member(IdDeq;x;faulty)] ∈ bag(Id)
31. (∀x∈bs.(loc(fst(snd(x))) = loc(e) ∈ Id)
∧ <<<n, 0>, snd(snd(x))>, fst(x)> ∈ new_23_sig_vote'base(Cmd;notify;propose;f)(fst(snd(x))))
32. l-ordered(Id × E × Cmd;x,y.(fst(snd(x)) <loc fst(snd(y)));bs)
33. (∀x∈bs.e ≤loc fst(snd(x)) )
34. ((coeff * flrs) + 1) ≤ ||bs||
⊢ (((coeff * flrs) + 1) ≤ ||mapfilter(λe.<snd(msgval(e)), e, snd(fst(msgval(e)))>;
λe.new_23_sig_vote_with_ballot(Cmd;notify;propose;f;es;e;n;0);
[e, fst(snd(last(bs)))])||)
∧ (∀x∈mapfilter(λe.<snd(msgval(e)), e, snd(fst(msgval(e)))>;
λe.new_23_sig_vote_with_ballot(Cmd;notify;propose;f;es;e;n;0);
[e, fst(snd(last(bs)))]).(loc(fst(snd(x))) = loc(e) ∈ Id)
∧ e ≤loc fst(snd(x))
∧ <<<n, 0>, snd(snd(x))>, fst(x)> ∈ new_23_sig_vote'base(Cmd;notify;propose;f)(fst(snd(x))))
∧ l-ordered(Id
× E
× Cmd;x,y.(fst(snd(x)) <loc fst(snd(y)));mapfilter(λe.<snd(msgval(e)), e, snd(fst(msgval(e)))>;
λe.new_23_sig_vote_with_ballot(Cmd;notify;propose;f;es;e;n;0);
[e, fst(snd(last(bs)))]))
∧ (∀e'∈[e, fst(snd(last(mapfilter(λe.<snd(msgval(e)), e, snd(fst(msgval(e)))>;
λe.new_23_sig_vote_with_ballot(Cmd;notify;propose;f;es;e;n;0);
[e, fst(snd(last(bs)))]))))].
(↑new_23_sig_vote_with_ballot(Cmd;notify;propose;f;es;e';n;0))
⇒ (e' ∈ map(λx.(fst(snd(x)));mapfilter(λe.<snd(msgval(e)), e, snd(fst(msgval(e)))>;
λe.new_23_sig_vote_with_ballot(Cmd;notify;propose;f;es;e;n;0);
[e, fst(snd(last(bs)))]))))
∧ b_all(Id;[x∈reps|
¬bbag-deq-member(IdDeq;x;faulty)];i.(i
∈ map(λi.(fst(i));
mapfilter(λe.<snd(msgval(e)), e, snd(fst(msgval(e)))>;
...;
[e, fst(snd(last(bs)))]))))
BY
{ ((Assert ⌈¬↑null(bs)⌉⋅ THENA (BLemma `non_null_iff_length` THEN Auto THEN Assert ⌈0 ≤ (coeff * flrs)⌉⋅ THEN Auto))
THEN Auto
) }
1
1. Cmd : {T:Type| valueall-type(T)}
2. eq : EqDecider(Cmd)
3. reps : bag(Id)
4. clients : bag(Id)
5. coeff : {2...}
6. flrs : ℕ
7. propose : Atom List
8. notify : Atom List
9. slots : set-sig{i:l}(ℤ)
10. f : new_23_sig_headers_type{i:l}(Cmd;notify;propose)
11. (f propose) = (ℤ × Cmd) ∈ Type
12. (f notify) = (ℤ × Cmd) ∈ Type
13. (f ``new_23_sig decided``) = (ℤ × Cmd) ∈ Type
14. (f ``new_23_sig retry``) = (ℤ × ℤ × Cmd) ∈ Type
15. (f ``new_23_sig vote``) = (ℤ × ℤ × Cmd × Id) ∈ Type
16. f ∈ Name ─→ Type
17. es : EO+(Message(f))
18. e : E
19. n : ℤ
20. c : Cmd
21. faulty : bag(Id)
22. msgs-interface-delivered-with-omissions(f;es;new_23_sig_main();faulty;flrs;reps)@i
23. bag-no-repeats(Id;reps)@i
24. #(reps) = ((coeff * flrs) + flrs + 1) ∈ ℤ@i
25. loc(e) ↓∈ reps@i
26. ¬loc(e) ↓∈ faulty@i
27. <n, c> ∈ new_23_sig_Proposal(Cmd;notify;propose;f)(e)@i
28. ¬↑(set-sig-member(slots) n new_23_sig_ReplicaStateFun(Cmd;notify;propose;slots;f;es;e))@i
29. bs : (Id × E × Cmd) List
30. bag-map(λi.(fst(i));bs) = [x∈reps|¬bbag-deq-member(IdDeq;x;faulty)] ∈ bag(Id)
31. (∀x∈bs.(loc(fst(snd(x))) = loc(e) ∈ Id)
∧ <<<n, 0>, snd(snd(x))>, fst(x)> ∈ new_23_sig_vote'base(Cmd;notify;propose;f)(fst(snd(x))))
32. l-ordered(Id × E × Cmd;x,y.(fst(snd(x)) <loc fst(snd(y)));bs)
33. (∀x∈bs.e ≤loc fst(snd(x)) )
34. ((coeff * flrs) + 1) ≤ ||bs||
35. ¬↑null(bs)
⊢ ((coeff * flrs) + 1) ≤ ||mapfilter(λe.<snd(msgval(e)), e, snd(fst(msgval(e)))>;
λe.new_23_sig_vote_with_ballot(Cmd;notify;propose;f;es;e;n;0);
[e, fst(snd(last(bs)))])||
2
1. Cmd : {T:Type| valueall-type(T)}
2. eq : EqDecider(Cmd)
3. reps : bag(Id)
4. clients : bag(Id)
5. coeff : {2...}
6. flrs : ℕ
7. propose : Atom List
8. notify : Atom List
9. slots : set-sig{i:l}(ℤ)
10. f : new_23_sig_headers_type{i:l}(Cmd;notify;propose)
11. (f propose) = (ℤ × Cmd) ∈ Type
12. (f notify) = (ℤ × Cmd) ∈ Type
13. (f ``new_23_sig decided``) = (ℤ × Cmd) ∈ Type
14. (f ``new_23_sig retry``) = (ℤ × ℤ × Cmd) ∈ Type
15. (f ``new_23_sig vote``) = (ℤ × ℤ × Cmd × Id) ∈ Type
16. f ∈ Name ─→ Type
17. es : EO+(Message(f))
18. e : E
19. n : ℤ
20. c : Cmd
21. faulty : bag(Id)
22. msgs-interface-delivered-with-omissions(f;es;new_23_sig_main();faulty;flrs;reps)@i
23. bag-no-repeats(Id;reps)@i
24. #(reps) = ((coeff * flrs) + flrs + 1) ∈ ℤ@i
25. loc(e) ↓∈ reps@i
26. ¬loc(e) ↓∈ faulty@i
27. <n, c> ∈ new_23_sig_Proposal(Cmd;notify;propose;f)(e)@i
28. ¬↑(set-sig-member(slots) n new_23_sig_ReplicaStateFun(Cmd;notify;propose;slots;f;es;e))@i
29. bs : (Id × E × Cmd) List
30. bag-map(λi.(fst(i));bs) = [x∈reps|¬bbag-deq-member(IdDeq;x;faulty)] ∈ bag(Id)
31. (∀x∈bs.(loc(fst(snd(x))) = loc(e) ∈ Id)
∧ <<<n, 0>, snd(snd(x))>, fst(x)> ∈ new_23_sig_vote'base(Cmd;notify;propose;f)(fst(snd(x))))
32. l-ordered(Id × E × Cmd;x,y.(fst(snd(x)) <loc fst(snd(y)));bs)
33. (∀x∈bs.e ≤loc fst(snd(x)) )
34. ((coeff * flrs) + 1) ≤ ||bs||
35. ¬↑null(bs)
36. ((coeff * flrs) + 1) ≤ ||mapfilter(λe.<snd(msgval(e)), e, snd(fst(msgval(e)))>;
λe.new_23_sig_vote_with_ballot(Cmd;notify;propose;f;es;e;n;0);
[e, fst(snd(last(bs)))])||
⊢ (∀x∈mapfilter(λe.<snd(msgval(e)), e, snd(fst(msgval(e)))>;
λe.new_23_sig_vote_with_ballot(Cmd;notify;propose;f;es;e;n;0);
[e, fst(snd(last(bs)))]).(loc(fst(snd(x))) = loc(e) ∈ Id)
∧ e ≤loc fst(snd(x))
∧ <<<n, 0>, snd(snd(x))>, fst(x)> ∈ new_23_sig_vote'base(Cmd;notify;propose;f)(fst(snd(x))))
3
1. Cmd : {T:Type| valueall-type(T)}
2. eq : EqDecider(Cmd)
3. reps : bag(Id)
4. clients : bag(Id)
5. coeff : {2...}
6. flrs : ℕ
7. propose : Atom List
8. notify : Atom List
9. slots : set-sig{i:l}(ℤ)
10. f : new_23_sig_headers_type{i:l}(Cmd;notify;propose)
11. (f propose) = (ℤ × Cmd) ∈ Type
12. (f notify) = (ℤ × Cmd) ∈ Type
13. (f ``new_23_sig decided``) = (ℤ × Cmd) ∈ Type
14. (f ``new_23_sig retry``) = (ℤ × ℤ × Cmd) ∈ Type
15. (f ``new_23_sig vote``) = (ℤ × ℤ × Cmd × Id) ∈ Type
16. f ∈ Name ─→ Type
17. es : EO+(Message(f))
18. e : E
19. n : ℤ
20. c : Cmd
21. faulty : bag(Id)
22. msgs-interface-delivered-with-omissions(f;es;new_23_sig_main();faulty;flrs;reps)@i
23. bag-no-repeats(Id;reps)@i
24. #(reps) = ((coeff * flrs) + flrs + 1) ∈ ℤ@i
25. loc(e) ↓∈ reps@i
26. ¬loc(e) ↓∈ faulty@i
27. <n, c> ∈ new_23_sig_Proposal(Cmd;notify;propose;f)(e)@i
28. ¬↑(set-sig-member(slots) n new_23_sig_ReplicaStateFun(Cmd;notify;propose;slots;f;es;e))@i
29. bs : (Id × E × Cmd) List
30. bag-map(λi.(fst(i));bs) = [x∈reps|¬bbag-deq-member(IdDeq;x;faulty)] ∈ bag(Id)
31. (∀x∈bs.(loc(fst(snd(x))) = loc(e) ∈ Id)
∧ <<<n, 0>, snd(snd(x))>, fst(x)> ∈ new_23_sig_vote'base(Cmd;notify;propose;f)(fst(snd(x))))
32. l-ordered(Id × E × Cmd;x,y.(fst(snd(x)) <loc fst(snd(y)));bs)
33. (∀x∈bs.e ≤loc fst(snd(x)) )
34. ((coeff * flrs) + 1) ≤ ||bs||
35. ¬↑null(bs)
36. ((coeff * flrs) + 1) ≤ ||mapfilter(λe.<snd(msgval(e)), e, snd(fst(msgval(e)))>;
λe.new_23_sig_vote_with_ballot(Cmd;notify;propose;f;es;e;n;0);
[e, fst(snd(last(bs)))])||
37. (∀x∈mapfilter(λe.<snd(msgval(e)), e, snd(fst(msgval(e)))>;
λe.new_23_sig_vote_with_ballot(Cmd;notify;propose;f;es;e;n;0);
[e, fst(snd(last(bs)))]).(loc(fst(snd(x))) = loc(e) ∈ Id)
∧ e ≤loc fst(snd(x))
∧ <<<n, 0>, snd(snd(x))>, fst(x)> ∈ new_23_sig_vote'base(Cmd;notify;propose;f)(fst(snd(x))))
⊢ l-ordered(Id
× E
× Cmd;x,y.(fst(snd(x)) <loc fst(snd(y)));mapfilter(λe.<snd(msgval(e)), e, snd(fst(msgval(e)))>;
λe.new_23_sig_vote_with_ballot(Cmd;notify;propose;f;es;e;n;0);
[e, fst(snd(last(bs)))]))
4
1. Cmd : {T:Type| valueall-type(T)}
2. eq : EqDecider(Cmd)
3. reps : bag(Id)
4. clients : bag(Id)
5. coeff : {2...}
6. flrs : ℕ
7. propose : Atom List
8. notify : Atom List
9. slots : set-sig{i:l}(ℤ)
10. f : new_23_sig_headers_type{i:l}(Cmd;notify;propose)
11. (f propose) = (ℤ × Cmd) ∈ Type
12. (f notify) = (ℤ × Cmd) ∈ Type
13. (f ``new_23_sig decided``) = (ℤ × Cmd) ∈ Type
14. (f ``new_23_sig retry``) = (ℤ × ℤ × Cmd) ∈ Type
15. (f ``new_23_sig vote``) = (ℤ × ℤ × Cmd × Id) ∈ Type
16. f ∈ Name ─→ Type
17. es : EO+(Message(f))
18. e : E
19. n : ℤ
20. c : Cmd
21. faulty : bag(Id)
22. msgs-interface-delivered-with-omissions(f;es;new_23_sig_main();faulty;flrs;reps)@i
23. bag-no-repeats(Id;reps)@i
24. #(reps) = ((coeff * flrs) + flrs + 1) ∈ ℤ@i
25. loc(e) ↓∈ reps@i
26. ¬loc(e) ↓∈ faulty@i
27. <n, c> ∈ new_23_sig_Proposal(Cmd;notify;propose;f)(e)@i
28. ¬↑(set-sig-member(slots) n new_23_sig_ReplicaStateFun(Cmd;notify;propose;slots;f;es;e))@i
29. bs : (Id × E × Cmd) List
30. bag-map(λi.(fst(i));bs) = [x∈reps|¬bbag-deq-member(IdDeq;x;faulty)] ∈ bag(Id)
31. (∀x∈bs.(loc(fst(snd(x))) = loc(e) ∈ Id)
∧ <<<n, 0>, snd(snd(x))>, fst(x)> ∈ new_23_sig_vote'base(Cmd;notify;propose;f)(fst(snd(x))))
32. l-ordered(Id × E × Cmd;x,y.(fst(snd(x)) <loc fst(snd(y)));bs)
33. (∀x∈bs.e ≤loc fst(snd(x)) )
34. ((coeff * flrs) + 1) ≤ ||bs||
35. ¬↑null(bs)
36. ((coeff * flrs) + 1) ≤ ||mapfilter(λe.<snd(msgval(e)), e, snd(fst(msgval(e)))>;
λe.new_23_sig_vote_with_ballot(Cmd;notify;propose;f;es;e;n;0);
[e, fst(snd(last(bs)))])||
37. (∀x∈mapfilter(λe.<snd(msgval(e)), e, snd(fst(msgval(e)))>;
λe.new_23_sig_vote_with_ballot(Cmd;notify;propose;f;es;e;n;0);
[e, fst(snd(last(bs)))]).(loc(fst(snd(x))) = loc(e) ∈ Id)
∧ e ≤loc fst(snd(x))
∧ <<<n, 0>, snd(snd(x))>, fst(x)> ∈ new_23_sig_vote'base(Cmd;notify;propose;f)(fst(snd(x))))
38. l-ordered(Id
× E
× Cmd;x,y.(fst(snd(x)) <loc fst(snd(y)));mapfilter(λe.<snd(msgval(e)), e, snd(fst(msgval(e)))>;
λe.new_23_sig_vote_with_ballot(Cmd;notify;propose;f;es;e;n;0);
[e, fst(snd(last(bs)))]))
⊢ (∀e'∈[e, fst(snd(last(mapfilter(λe.<snd(msgval(e)), e, snd(fst(msgval(e)))>;
λe.new_23_sig_vote_with_ballot(Cmd;notify;propose;f;es;e;n;0);
[e, fst(snd(last(bs)))]))))].
(↑new_23_sig_vote_with_ballot(Cmd;notify;propose;f;es;e';n;0))
⇒ (e' ∈ map(λx.(fst(snd(x)));mapfilter(λe.<snd(msgval(e)), e, snd(fst(msgval(e)))>;
λe.new_23_sig_vote_with_ballot(Cmd;notify;propose;f;es;e;n;0);
[e, fst(snd(last(bs)))]))))
5
1. Cmd : {T:Type| valueall-type(T)}
2. eq : EqDecider(Cmd)
3. reps : bag(Id)
4. clients : bag(Id)
5. coeff : {2...}
6. flrs : ℕ
7. propose : Atom List
8. notify : Atom List
9. slots : set-sig{i:l}(ℤ)
10. f : new_23_sig_headers_type{i:l}(Cmd;notify;propose)
11. (f propose) = (ℤ × Cmd) ∈ Type
12. (f notify) = (ℤ × Cmd) ∈ Type
13. (f ``new_23_sig decided``) = (ℤ × Cmd) ∈ Type
14. (f ``new_23_sig retry``) = (ℤ × ℤ × Cmd) ∈ Type
15. (f ``new_23_sig vote``) = (ℤ × ℤ × Cmd × Id) ∈ Type
16. f ∈ Name ─→ Type
17. es : EO+(Message(f))
18. e : E
19. n : ℤ
20. c : Cmd
21. faulty : bag(Id)
22. msgs-interface-delivered-with-omissions(f;es;new_23_sig_main();faulty;flrs;reps)@i
23. bag-no-repeats(Id;reps)@i
24. #(reps) = ((coeff * flrs) + flrs + 1) ∈ ℤ@i
25. loc(e) ↓∈ reps@i
26. ¬loc(e) ↓∈ faulty@i
27. <n, c> ∈ new_23_sig_Proposal(Cmd;notify;propose;f)(e)@i
28. ¬↑(set-sig-member(slots) n new_23_sig_ReplicaStateFun(Cmd;notify;propose;slots;f;es;e))@i
29. bs : (Id × E × Cmd) List
30. bag-map(λi.(fst(i));bs) = [x∈reps|¬bbag-deq-member(IdDeq;x;faulty)] ∈ bag(Id)
31. (∀x∈bs.(loc(fst(snd(x))) = loc(e) ∈ Id)
∧ <<<n, 0>, snd(snd(x))>, fst(x)> ∈ new_23_sig_vote'base(Cmd;notify;propose;f)(fst(snd(x))))
32. l-ordered(Id × E × Cmd;x,y.(fst(snd(x)) <loc fst(snd(y)));bs)
33. (∀x∈bs.e ≤loc fst(snd(x)) )
34. ((coeff * flrs) + 1) ≤ ||bs||
35. ¬↑null(bs)
36. ((coeff * flrs) + 1) ≤ ||mapfilter(λe.<snd(msgval(e)), e, snd(fst(msgval(e)))>;
λe.new_23_sig_vote_with_ballot(Cmd;notify;propose;f;es;e;n;0);
[e, fst(snd(last(bs)))])||
37. (∀x∈mapfilter(λe.<snd(msgval(e)), e, snd(fst(msgval(e)))>;
λe.new_23_sig_vote_with_ballot(Cmd;notify;propose;f;es;e;n;0);
[e, fst(snd(last(bs)))]).(loc(fst(snd(x))) = loc(e) ∈ Id)
∧ e ≤loc fst(snd(x))
∧ <<<n, 0>, snd(snd(x))>, fst(x)> ∈ new_23_sig_vote'base(Cmd;notify;propose;f)(fst(snd(x))))
38. l-ordered(Id
× E
× Cmd;x,y.(fst(snd(x)) <loc fst(snd(y)));mapfilter(λe.<snd(msgval(e)), e, snd(fst(msgval(e)))>;
λe.new_23_sig_vote_with_ballot(Cmd;notify;propose;f;es;e;n;0);
[e, fst(snd(last(bs)))]))
39. (∀e'∈[e, fst(snd(last(mapfilter(λe.<snd(msgval(e)), e, snd(fst(msgval(e)))>;
λe.new_23_sig_vote_with_ballot(Cmd;notify;propose;f;es;e;n;0);
[e, fst(snd(last(bs)))]))))].
(↑new_23_sig_vote_with_ballot(Cmd;notify;propose;f;es;e';n;0))
⇒ (e' ∈ map(λx.(fst(snd(x)));mapfilter(λe.<snd(msgval(e)), e, snd(fst(msgval(e)))>;
λe.new_23_sig_vote_with_ballot(Cmd;notify;propose;f;es;e;n;0);
[e, fst(snd(last(bs)))]))))
⊢ b_all(Id;[x∈reps|
¬bbag-deq-member(IdDeq;x;faulty)];i.(i
∈ map(λi.(fst(i));
mapfilter(λe.<snd(msgval(e)), e, snd(fst(msgval(e)))>;
...;
[e, fst(snd(last(bs)))]))))
Latex:
Latex:
1. Cmd : \{T:Type| valueall-type(T)\}
2. eq : EqDecider(Cmd)
3. reps : bag(Id)
4. clients : bag(Id)
5. coeff : \{2...\}
6. flrs : \mBbbN{}
7. propose : Atom List
8. notify : Atom List
9. slots : set-sig\{i:l\}(\mBbbZ{})
10. f : new\_23\_sig\_headers\_type\{i:l\}(Cmd;notify;propose)
11. (f propose) = (\mBbbZ{} \mtimes{} Cmd)
12. (f notify) = (\mBbbZ{} \mtimes{} Cmd)
13. (f ``new\_23\_sig decided``) = (\mBbbZ{} \mtimes{} Cmd)
14. (f ``new\_23\_sig retry``) = (\mBbbZ{} \mtimes{} \mBbbZ{} \mtimes{} Cmd)
15. (f ``new\_23\_sig vote``) = (\mBbbZ{} \mtimes{} \mBbbZ{} \mtimes{} Cmd \mtimes{} Id)
16. f \mmember{} Name {}\mrightarrow{} Type
17. es : EO+(Message(f))
18. e : E
19. n : \mBbbZ{}
20. c : Cmd
21. faulty : bag(Id)
22. msgs-interface-delivered-with-omissions(f;es;new\_23\_sig\_main();faulty;flrs;reps)@i
23. bag-no-repeats(Id;reps)@i
24. \#(reps) = ((coeff * flrs) + flrs + 1)@i
25. loc(e) \mdownarrow{}\mmember{} reps@i
26. \mneg{}loc(e) \mdownarrow{}\mmember{} faulty@i
27. <n, c> \mmember{} new\_23\_sig\_Proposal(Cmd;notify;propose;f)(e)@i
28. \mneg{}\muparrow{}(set-sig-member(slots) n new\_23\_sig\_ReplicaStateFun(Cmd;notify;propose;slots;f;es;e))@i
29. bs : (Id \mtimes{} E \mtimes{} Cmd) List
30. bag-map(\mlambda{}i.(fst(i));bs) = [x\mmember{}reps|\mneg{}\msubb{}bag-deq-member(IdDeq;x;faulty)]
31. (\mforall{}x\mmember{}bs.(loc(fst(snd(x))) = loc(e))
\mwedge{} <<<n, 0>, snd(snd(x))>, fst(x)> \mmember{} new\_23\_sig\_vote'base(Cmd;notify;propose;f)(fst(snd(x))))
32. l-ordered(Id \mtimes{} E \mtimes{} Cmd;x,y.(fst(snd(x)) <loc fst(snd(y)));bs)
33. (\mforall{}x\mmember{}bs.e \mleq{}loc fst(snd(x)) )
34. ((coeff * flrs) + 1) \mleq{} ||bs||
\mvdash{} (((coeff * flrs) + 1) \mleq{} ||mapfilter(\mlambda{}e.<snd(msgval(e)), e, snd(fst(msgval(e)))>
\mlambda{}e.new\_23\_sig\_vote\_with\_ballot(Cmd;notify;propose;f;es;e;n;0);
[e, fst(snd(last(bs)))])||)
\mwedge{} (\mforall{}x\mmember{}mapfilter(\mlambda{}e.<snd(msgval(e)), e, snd(fst(msgval(e)))>
\mlambda{}e.new\_23\_sig\_vote\_with\_ballot(Cmd;notify;propose;f;es;e;n;0);
[e, fst(snd(last(bs)))]).(loc(fst(snd(x))) = loc(e))
\mwedge{} e \mleq{}loc fst(snd(x))
\mwedge{} <<<n, 0>, snd(snd(x))>, fst(x)> \mmember{} new\_23\_sig\_vote'base(Cmd;notify;propose;f)(fst(snd(x))))
\mwedge{} l-ordered(Id
\mtimes{} E
\mtimes{} Cmd;x,y.(fst(snd(x)) <loc fst(snd(y)));mapfilter(\mlambda{}e.<snd(msgval(e)), e, snd(fst(msgval(e)))>
\mlambda{}e....;
[e, fst(snd(last(bs)))]))
\mwedge{} (\mforall{}e'\mmember{}[e, fst(snd(last(mapfilter(\mlambda{}e.<snd(msgval(e)), e, snd(fst(msgval(e)))>
\mlambda{}e.new\_23\_sig\_vote\_with\_ballot(Cmd;notify;propose;f;es;e;n;0);
[e, fst(snd(last(bs)))]))))].
(\muparrow{}new\_23\_sig\_vote\_with\_ballot(Cmd;notify;propose;f;es;e';n;0))
{}\mRightarrow{} (e' \mmember{} map(\mlambda{}x.(fst(snd(x)));
mapfilter(\mlambda{}e.<snd(msgval(e)), e, snd(fst(msgval(e)))>
\mlambda{}e.new\_23\_sig\_vote\_with\_ballot(Cmd;notify;propose;f;es;e;n;0);
[e, fst(snd(last(bs)))]))))
\mwedge{} b\_all(Id;[x\mmember{}reps|
\mneg{}\msubb{}bag-deq-member(IdDeq;x;faulty)];i.(i
\mmember{} map(\mlambda{}i.(fst(i));
mapfilter(\mlambda{}e.<snd(msgval(e))
, e
, snd(fst(msgval(e)))>
\mlambda{}e....;
[e, fst(snd(last(bs)))]))))
By
Latex:
((Assert \mkleeneopen{}\mneg{}\muparrow{}null(bs)\mkleeneclose{}\mcdot{}
THENA (BLemma `non\_null\_iff\_length` THEN Auto THEN Assert \mkleeneopen{}0 \mleq{} (coeff * flrs)\mkleeneclose{}\mcdot{} THEN Auto)
)
THEN Auto
)
Home
Index