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Step * 1 of Lemma proper-maps-compact

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

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Latex:

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Latex:
.....wf..... 
1.  I  :  Interval
2.  J  :  Interval
3.  f  :  I  {}\mrightarrow{}\mBbbR{}
4.  iproper(J)
5.  \mforall{}n:\{n:\mBbbN{}\msupplus{}|  icompact(i-approx(I;n))\} 
          \mexists{}m:\{m:\mBbbN{}\msupplus{}|  icompact(i-approx(J;m))\}  .  \mforall{}x:\{x:\mBbbR{}|  x  \mmember{}  i-approx(I;n)\}  .  (f[x]  \mmember{}  i-approx(J;m))
6.  n  :  \{n:\mBbbN{}\msupplus{}|  icompact(i-approx(I;n))  \mwedge{}  iproper(i-approx(I;n))\} 
7.  m  :  \{m:\mBbbN{}\msupplus{}|  icompact(i-approx(J;m))\} 
8.  \mforall{}x:\{x:\mBbbR{}|  x  \mmember{}  i-approx(I;n)\}  .  (f[x]  \mmember{}  i-approx(J;m))
\mvdash{}  m  +  1  \mmember{}  \{m:\mBbbN{}\msupplus{}|  icompact(i-approx(J;m))  \mwedge{}  iproper(i-approx(J;m))\} 


By

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Latex:
(D  -2  THEN  InstLemma  `iproper-approx`  [\mkleeneopen{}J\mkleeneclose{};\mkleeneopen{}m\mkleeneclose{}]\mcdot{}  THEN  Auto)

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