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Step * 1 1 1 of Lemma continuous-maps-compact

.....wf..... 
1. I : Interval
2. f : I ⟶ℝ
3. iproper(I)
4. f[x] (proper)continuous for x ∈ I
5. n : {n:ℕ+| icompact(i-approx(I;n))} 
⊢ n + 1 ∈ {n:ℕ+| icompact(i-approx(I;n)) ∧ iproper(i-approx(I;n))} 
BY
{ (D -1 THEN InstLemma `iproper-approx` [⌜I⌝;⌜n⌝]⋅ THEN Auto) }

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Latex:

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Latex:
.....wf..... 
1.  I  :  Interval
2.  f  :  I  {}\mrightarrow{}\mBbbR{}
3.  iproper(I)
4.  f[x]  (proper)continuous  for  x  \mmember{}  I
5.  n  :  \{n:\mBbbN{}\msupplus{}|  icompact(i-approx(I;n))\} 
\mvdash{}  n  +  1  \mmember{}  \{n:\mBbbN{}\msupplus{}|  icompact(i-approx(I;n))  \mwedge{}  iproper(i-approx(I;n))\} 


By

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Latex:
(D  -1  THEN  InstLemma  `iproper-approx`  [\mkleeneopen{}I\mkleeneclose{};\mkleeneopen{}n\mkleeneclose{}]\mcdot{}  THEN  Auto)

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