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Step * of Lemma decidable__cs-inning-committed-some

∀[V:Type]
  ((∀v,v':V.  Dec(v = v' ∈ V))
  ⇒ (∀A:Id List. ∀W:{a:Id| (a ∈ A)}  List List.
        (one-intersection(A;W) ⇒ (∀s:ConsensusState. ∀i:ℤ.  Dec(∃v:V. in state s, inning i has committed v)))))
BY
{ (Auto
   THEN (InstLemma `cs-inning-committed-some1` [⌈V⌉;⌈A⌉;⌈W⌉;⌈s⌉;⌈i⌉]⋅ THENA Auto)
   THEN D -1
   THEN RWO "-1" 0
   THEN Auto) }

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Latex:


\mforall{}[V:Type]
    ((\mforall{}v,v':V.    Dec(v  =  v'))
    {}\mRightarrow{}  (\mforall{}A:Id  List.  \mforall{}W:\{a:Id|  (a  \mmember{}  A)\}    List  List.
                (one-intersection(A;W)
                {}\mRightarrow{}  (\mforall{}s:ConsensusState.  \mforall{}i:\mBbbZ{}.    Dec(\mexists{}v:V.  in  state  s,  inning  i  has  committed  v)))))


By

(Auto
  THEN  (InstLemma  `cs-inning-committed-some1`  [\mkleeneopen{}V\mkleeneclose{};\mkleeneopen{}A\mkleeneclose{};\mkleeneopen{}W\mkleeneclose{};\mkleeneopen{}s\mkleeneclose{};\mkleeneopen{}i\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  D  -1
  THEN  RWO  "-1"  0
  THEN  Auto)

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