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Step * of Lemma I-norm-rleq

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∀[I:{I:Interval| icompact(I)} ]. ∀[f:{x:ℝ| x ∈ I}  ⟶ ℝ].
  ∀[c:ℝ]. ||f[x]||_x:I ≤ c supposing ∀[x:{r:ℝ| r ∈ I} ]. (|f[x]| ≤ c) 
  supposing ∀x,y:{x:ℝ| x ∈ I} .  ((x = y) ⇒ (f[x] = f[y]))
BY
{ (Auto THEN Unfold `I-norm` 0 THEN (InstLemma  `range_sup-bound` [⌜I⌝;⌜λ2x.|f[x]|⌝]⋅ THENM BHyp -1) THEN Auto) }

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Latex:

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Latex:
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\mforall{}[I:\{I:Interval|  icompact(I)\}  ].  \mforall{}[f:\{x:\mBbbR{}|  x  \mmember{}  I\}    {}\mrightarrow{}  \mBbbR{}].
    \mforall{}[c:\mBbbR{}].  ||f[x]||\_x:I  \mleq{}  c  supposing  \mforall{}[x:\{r:\mBbbR{}|  r  \mmember{}  I\}  ].  (|f[x]|  \mleq{}  c) 
    supposing  \mforall{}x,y:\{x:\mBbbR{}|  x  \mmember{}  I\}  .    ((x  =  y)  {}\mRightarrow{}  (f[x]  =  f[y]))


By

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Latex:
(Auto
  THEN  Unfold  `I-norm`  0
  THEN  (InstLemma    `range\_sup-bound`  [\mkleeneopen{}I\mkleeneclose{};\mkleeneopen{}\mlambda{}\msubtwo{}x.|f[x]|\mkleeneclose{}]\mcdot{}  THENM  BHyp  -1)
  THEN  Auto)

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