Step
*
of Lemma
new_23_sig_vote_with_ballot_wf
∀[Cmd:ValueAllType]. ∀[propose,notify:Atom List]. ∀[f:new_23_sig_headers_type{i:l}(Cmd;notify;propose)].
∀[es:EO+(Message(f))]. ∀[e:E]. ∀[n,r:ℤ].
(new_23_sig_vote_with_ballot(Cmd;notify;propose;f;es;e;n;r) ∈ 𝔹)
BY
{ (Unfold `vatype` 0
THEN (UnivCD THENA Auto)
THEN AddMessageHeaderTypes
THEN UnfoldAtAddr [2] 0
THEN (BoolCase ⌈e ∈b new_23_sig_vote'base(Cmd;notify;propose;f)⌉⋅ THENA Auto)) }
1
1. Cmd : {T:Type| valueall-type(T)}
2. propose : Atom List
3. notify : Atom List
4. f : new_23_sig_headers_type{i:l}(Cmd;notify;propose)
5. es : EO+(Message(f))
6. e : E
7. n : ℤ
8. r : ℤ
9. ((f propose) = (ℤ × Cmd) ∈ Type)
∧ ((f notify) = (ℤ × Cmd) ∈ Type)
∧ ((f ``new_23_sig decided``) = (ℤ × Cmd) ∈ Type)
∧ ((f ``new_23_sig retry``) = (ℤ × ℤ × Cmd) ∈ Type)
∧ ((f ``new_23_sig vote``) = (ℤ × ℤ × Cmd × Id) ∈ Type)
10. f ∈ Name ─→ Type
11. ↑e ∈b new_23_sig_vote'base(Cmd;notify;propose;f)
⊢ (fst(fst(fst(msgval(e)))) =z n) ∧b (snd(fst(fst(msgval(e)))) =z r) ∈ 𝔹
2
1. Cmd : {T:Type| valueall-type(T)}
2. propose : Atom List
3. notify : Atom List
4. f : new_23_sig_headers_type{i:l}(Cmd;notify;propose)
5. es : EO+(Message(f))
6. e : E
7. ¬↑e ∈b new_23_sig_vote'base(Cmd;notify;propose;f)
8. n : ℤ
9. r : ℤ
10. ((f propose) = (ℤ × Cmd) ∈ Type)
∧ ((f notify) = (ℤ × Cmd) ∈ Type)
∧ ((f ``new_23_sig decided``) = (ℤ × Cmd) ∈ Type)
∧ ((f ``new_23_sig retry``) = (ℤ × ℤ × Cmd) ∈ Type)
∧ ((f ``new_23_sig vote``) = (ℤ × ℤ × Cmd × Id) ∈ Type)
11. f ∈ Name ─→ Type
⊢ ff ∈ 𝔹
Latex:
Latex:
\mforall{}[Cmd:ValueAllType]. \mforall{}[propose,notify:Atom List].
\mforall{}[f:new\_23\_sig\_headers\_type\{i:l\}(Cmd;notify;propose)]. \mforall{}[es:EO+(Message(f))]. \mforall{}[e:E]. \mforall{}[n,r:\mBbbZ{}].
(new\_23\_sig\_vote\_with\_ballot(Cmd;notify;propose;f;es;e;n;r) \mmember{} \mBbbB{})
By
Latex:
(Unfold `vatype` 0
THEN (UnivCD THENA Auto)
THEN AddMessageHeaderTypes
THEN UnfoldAtAddr [2] 0
THEN (BoolCase \mkleeneopen{}e \mmember{}\msubb{} new\_23\_sig\_vote'base(Cmd;notify;propose;f)\mkleeneclose{}\mcdot{} THENA Auto))
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