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Step * 2 1 of Lemma near-log-exists


1. ∀a:{a:ℝ| r1 ≤ a} . ∀N:ℕ+.  ∃m:ℕ+. (∃z:ℤ [(|(r(z))/m - rlog(a)| ≤ (r1/r(N)))])
2. a : {a:ℝ| r0 < a} 
3. N : ℕ+
⊢ ∃m:ℕ+. (∃z:ℤ [(|(r(z))/m - rlog(a)| ≤ (r1/r(N)))])
BY
{ (InstLemma `rabs-rlog-difference-bound` [⌜a⌝;⌜r1⌝]⋅ THENA Auto) }

1
1. ∀a:{a:ℝ| r1 ≤ a} . ∀N:ℕ+.  ∃m:ℕ+. (∃z:ℤ [(|(r(z))/m - rlog(a)| ≤ (r1/r(N)))])
2. a : {a:ℝ| r0 < a} 
3. N : ℕ+
4. |rlog(r1) - rlog(a)| ≤ (|r1 - a|/rmin(a;r1))
⊢ ∃m:ℕ+. (∃z:ℤ [(|(r(z))/m - rlog(a)| ≤ (r1/r(N)))])

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Latex:

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Latex:

1.  \mforall{}a:\{a:\mBbbR{}|  r1  \mleq{}  a\}  .  \mforall{}N:\mBbbN{}\msupplus{}.    \mexists{}m:\mBbbN{}\msupplus{}.  (\mexists{}z:\mBbbZ{}  [(|(r(z))/m  -  rlog(a)|  \mleq{}  (r1/r(N)))])
2.  a  :  \{a:\mBbbR{}|  r0  <  a\} 
3.  N  :  \mBbbN{}\msupplus{}
\mvdash{}  \mexists{}m:\mBbbN{}\msupplus{}.  (\mexists{}z:\mBbbZ{}  [(|(r(z))/m  -  rlog(a)|  \mleq{}  (r1/r(N)))])


By

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Latex:
(InstLemma  `rabs-rlog-difference-bound`  [\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}r1\mkleeneclose{}]\mcdot{}  THENA  Auto)

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