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Step * of Lemma I-norm_functionality_wrt_subinterval

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∀[I:{I:Interval| icompact(I)} ]. ∀[f:{x:ℝ| x ∈ I}  ⟶ ℝ].
  ∀[J:{J:Interval| icompact(J)} ]. ||f[x]||_x:J ≤ ||f[x]||_x:I supposing J ⊆ I  
  supposing ∀x,y:{x:ℝ| x ∈ I} .  ((x = y) ⇒ (f[x] = f[y]))
BY
{ (Auto THEN BLemma `I-norm-rleq` THEN Auto THEN InstLemma `I-norm-bound`[⌜I⌝;⌜f⌝;⌜x⌝]⋅ 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{}[J:\{J:Interval|  icompact(J)\}  ].  ||f[x]||\_x:J  \mleq{}  ||f[x]||\_x:I  supposing  J  \msubseteq{}  I   
    supposing  \mforall{}x,y:\{x:\mBbbR{}|  x  \mmember{}  I\}  .    ((x  =  y)  {}\mRightarrow{}  (f[x]  =  f[y]))


By

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Latex:
(Auto  THEN  BLemma  `I-norm-rleq`  THEN  Auto  THEN  InstLemma  `I-norm-bound`[\mkleeneopen{}I\mkleeneclose{};\mkleeneopen{}f\mkleeneclose{};\mkleeneopen{}x\mkleeneclose{}]\mcdot{}  THEN  Auto)

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