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Step * of Lemma nearby-partition-sum-no-mc

∀I:Interval
  (icompact(I)
  ⇒ iproper(I)
  ⇒ (∀f:{f:I ⟶ℝ| ifun(f;I)} . ∀p:partition(I). ∀x:partition-choice(full-partition(I;p)). ∀alpha:{a:ℝ| r0 < a} .
        ∃e:{e:ℝ| r0 < e} 
         ∀q:partition(I). ∀y:partition-choice(full-partition(I;q)).
           (nearby-partitions(e;p;q)
           ⇒ (∀i:ℕ||p|| + 1. (|x[i] - y[i]| ≤ e))
           ⇒ (|S(f;full-partition(I;q)) - S(f;full-partition(I;p))| ≤ alpha))))
BY
{ (InstLemma `ifun-continuous` []
   THEN (RepeatFor 2 ((ParallelLast' THENA Auto)) THEN (D 0 THENA Auto) THEN (ParallelOp -2 THENA Auto))
   THEN RenameVar `mc' (-1)
   THEN InstLemma `nearby-partition-sum-ext` [⌜I⌝;⌜f⌝;⌜mc⌝]⋅
   THEN Auto) }

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Latex:

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Latex:
\mforall{}I:Interval
    (icompact(I)
    {}\mRightarrow{}  iproper(I)
    {}\mRightarrow{}  (\mforall{}f:\{f:I  {}\mrightarrow{}\mBbbR{}|  ifun(f;I)\}  .  \mforall{}p:partition(I).  \mforall{}x:partition-choice(full-partition(I;p)).
            \mforall{}alpha:\{a:\mBbbR{}|  r0  <  a\}  .
                \mexists{}e:\{e:\mBbbR{}|  r0  <  e\} 
                  \mforall{}q:partition(I).  \mforall{}y:partition-choice(full-partition(I;q)).
                      (nearby-partitions(e;p;q)
                      {}\mRightarrow{}  (\mforall{}i:\mBbbN{}||p||  +  1.  (|x[i]  -  y[i]|  \mleq{}  e))
                      {}\mRightarrow{}  (|S(f;full-partition(I;q))  -  S(f;full-partition(I;p))|  \mleq{}  alpha))))


By

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Latex:
(InstLemma  `ifun-continuous`  []
  THEN  (RepeatFor  2  ((ParallelLast'  THENA  Auto))
              THEN  (D  0  THENA  Auto)
              THEN  (ParallelOp  -2  THENA  Auto))
  THEN  RenameVar  `mc'  (-1)
  THEN  InstLemma  `nearby-partition-sum-ext`  [\mkleeneopen{}I\mkleeneclose{};\mkleeneopen{}f\mkleeneclose{};\mkleeneopen{}mc\mkleeneclose{}]\mcdot{}
  THEN  Auto)

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