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Step * 2 of Lemma rcos-seq-converges-to-half-pi


1. π/2(slower)
= (λn.eval m = 4 * n in
      (rcos-seq(exp-ratio(1;3164556962025316455;0;m;1000000000) + 1) m) ÷ 4)
∈ (ℕ+ ⟶ ℤ)
⊢ lim n→∞.rcos-seq(n) = π/2(slower)
BY
{ (Assert snd(TERMOF{rcos-seq-converges-ext:o, \\v:l}) ∈ lim n→∞.rcos-seq(n) = fst(TERMOF{rcos-seq-converges-ext:o,
                                                                                          \\v:l}) BY
         Auto) }

1
1. π/2(slower)
= (λn.eval m = 4 * n in
      (rcos-seq(exp-ratio(1;3164556962025316455;0;m;1000000000) + 1) m) ÷ 4)
∈ (ℕ+ ⟶ ℤ)
2. snd(TERMOF{rcos-seq-converges-ext:o, \\v:l}) ∈ lim n→∞.rcos-seq(n) = fst(TERMOF{rcos-seq-converges-ext:o, \\v:l})
⊢ lim n→∞.rcos-seq(n) = π/2(slower)

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Latex:

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Latex:

1.  \mpi{}/2(slower)
=  (\mlambda{}n.eval  m  =  4  *  n  in
            (rcos-seq(exp-ratio(1;3164556962025316455;0;m;1000000000)  +  1)  m)  \mdiv{}  4)
\mvdash{}  lim  n\mrightarrow{}\minfty{}.rcos-seq(n)  =  \mpi{}/2(slower)


By

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Latex:
(Assert  snd(TERMOF\{rcos-seq-converges-ext:o,  \mbackslash{}\mbackslash{}v:l\})
                \mmember{}  lim  n\mrightarrow{}\minfty{}.rcos-seq(n)  =  fst(TERMOF\{rcos-seq-converges-ext:o,  \mbackslash{}\mbackslash{}v:l\})  BY
              Auto)

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