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Step * 2 1 1 of Lemma cantor-to-interval_wf

.....assertion..... 
1. a : ℝ
2. b : ℝ
3. a ≤ b
4. f : ℕ ⟶ 𝔹
5. cantor-to-interval(a;b;f) = cantor-to-interval(a;b;f) ∈ {x:ℝ| lim n→∞.fst(cantor-interval(a;b;f;n)) = x} 
6. x : ℝ
7. lim n→∞.fst(cantor-interval(a;b;f;n)) = x
⊢ ∀n:ℕ. (a ≤ (fst(cantor-interval(a;b;f;n))))
BY
{ ((D 0 THENA Auto)
   THEN (InstLemma `cantor-interval-inclusion` [⌜a⌝;⌜b⌝;⌜f⌝;⌜0⌝;⌜n⌝]⋅ THENA Auto)
   THEN Unfold `cantor-interval` -1
   THEN Reduce (-1)
   THEN Fold `cantor-interval` (-1)
   THEN Auto) }

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Latex:

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Latex:
.....assertion..... 
1.  a  :  \mBbbR{}
2.  b  :  \mBbbR{}
3.  a  \mleq{}  b
4.  f  :  \mBbbN{}  {}\mrightarrow{}  \mBbbB{}
5.  cantor-to-interval(a;b;f)  =  cantor-to-interval(a;b;f)
6.  x  :  \mBbbR{}
7.  lim  n\mrightarrow{}\minfty{}.fst(cantor-interval(a;b;f;n))  =  x
\mvdash{}  \mforall{}n:\mBbbN{}.  (a  \mleq{}  (fst(cantor-interval(a;b;f;n))))


By

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Latex:
((D  0  THENA  Auto)
  THEN  (InstLemma  `cantor-interval-inclusion`  [\mkleeneopen{}a\mkleeneclose{};\mkleeneopen{}b\mkleeneclose{};\mkleeneopen{}f\mkleeneclose{};\mkleeneopen{}0\mkleeneclose{};\mkleeneopen{}n\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  Unfold  `cantor-interval`  -1
  THEN  Reduce  (-1)
  THEN  Fold  `cantor-interval`  (-1)
  THEN  Auto)

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