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Step * of Lemma rleq-range_sup-2

No Annotations
∀I:{I:Interval| icompact(I)} . ∀f:{x:ℝ| x ∈ I}  ⟶ ℝ.
  ∀[c:ℝ]. c ≤ sup{f[x] | x ∈ I} supposing ∃x:ℝ. ((x ∈ I) ∧ (c ≤ f[x])) 
  supposing ∀x,y:{x:ℝ| x ∈ I} .  ((x = y) ⇒ (f[x] = f[y]))
BY
{ (Auto THEN RepeatFor 2 (D -1) THEN RWO  "-1" 0 THEN Auto THEN InstLemma `rleq-range_sup` [⌜I⌝;⌜f⌝;⌜x⌝]⋅ THEN Auto) }

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Latex:

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Latex:
No  Annotations
\mforall{}I:\{I:Interval|  icompact(I)\}  .  \mforall{}f:\{x:\mBbbR{}|  x  \mmember{}  I\}    {}\mrightarrow{}  \mBbbR{}.
    \mforall{}[c:\mBbbR{}].  c  \mleq{}  sup\{f[x]  |  x  \mmember{}  I\}  supposing  \mexists{}x:\mBbbR{}.  ((x  \mmember{}  I)  \mwedge{}  (c  \mleq{}  f[x])) 
    supposing  \mforall{}x,y:\{x:\mBbbR{}|  x  \mmember{}  I\}  .    ((x  =  y)  {}\mRightarrow{}  (f[x]  =  f[y]))


By

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Latex:
(Auto
  THEN  RepeatFor  2  (D  -1)
  THEN  RWO    "-1"  0
  THEN  Auto
  THEN  InstLemma  `rleq-range\_sup`  [\mkleeneopen{}I\mkleeneclose{};\mkleeneopen{}f\mkleeneclose{};\mkleeneopen{}x\mkleeneclose{}]\mcdot{}
  THEN  Auto)

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