Step
*
1
2
of Lemma
cs-inning-committable-some1
1. [V] : Type
2. v : V@i
3. v' : V@i
4. ¬(v = v' ∈ V)@i
5. ∀v,v':V. Dec(v = v' ∈ V)@i
6. A : Id List@i
7. W : {a:Id| (a ∈ A)} List List@i
8. one-intersection(A;W)@i
9. s : ConsensusState@i
10. i : ℤ@i
11. L : V List
12. ∀v:V
(in state s, inning i could commit v
⇐⇒ (in state s, inning i could commit v ∧ (v ∈ L))
∨ (∃ws∈W. ∀a:{a:Id| (a ∈ A)} . ((a ∈ ws)
⇒ in state s, a has not completed inning i)))
13. (∃v∈L. in state s, inning i could commit v )@i
⊢ ∃v:V. in state s, inning i could commit v
BY
{ (RWO "l_exists_iff" (-1) THEN Auto THEN D -1 THEN Auto) }
Latex:
1. [V] : Type
2. v : V@i
3. v' : V@i
4. \mneg{}(v = v')@i
5. \mforall{}v,v':V. Dec(v = v')@i
6. A : Id List@i
7. W : \{a:Id| (a \mmember{} A)\} List List@i
8. one-intersection(A;W)@i
9. s : ConsensusState@i
10. i : \mBbbZ{}@i
11. L : V List
12. \mforall{}v:V
(in state s, inning i could commit v
\mLeftarrow{}{}\mRightarrow{} (in state s, inning i could commit v \mwedge{} (v \mmember{} L))
\mvee{} (\mexists{}ws\mmember{}W. \mforall{}a:\{a:Id| (a \mmember{} A)\} . ((a \mmember{} ws) {}\mRightarrow{} in state s, a has not completed inning i)))
13. (\mexists{}v\mmember{}L. in state s, inning i could commit v )@i
\mvdash{} \mexists{}v:V. in state s, inning i could commit v
By
(RWO "l\_exists\_iff" (-1) THEN Auto THEN D -1 THEN Auto)
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