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Step * of Lemma rabs-partition-sum

∀I:Interval
  (icompact(I)
  ⇒ (∀f:I ⟶ℝ. ∀p:partition(I). ∀y:partition-choice(full-partition(I;p)).
        (|S(f;full-partition(I;p))| ≤ S(λx.|f x|;full-partition(I;p)))))
BY
{ (Auto
   THEN Unfold `partition-sum` 0
   THEN Reduce 0
   THEN (GenConcl ⌜y = a ∈ (ℕ||p|| + 1 ⟶ {x:ℝ| x ∈ I} )⌝⋅ THENA Auto)
   THEN (Assert ||full-partition(I;p)|| = (||p|| + 2) ∈ ℤ BY
               (Unfold `full-partition` 0 THEN Auto'))) }

1
1. I : Interval
2. icompact(I)
3. f : I ⟶ℝ
4. p : partition(I)
5. y : partition-choice(full-partition(I;p))
6. a : ℕ||p|| + 1 ⟶ {x:ℝ| x ∈ I} 
7. y = a ∈ (ℕ||p|| + 1 ⟶ {x:ℝ| x ∈ I} )
8. ||full-partition(I;p)|| = (||p|| + 2) ∈ ℤ
⊢ |Σ{(f (a i)) * (full-partition(I;p)[i + 1] - full-partition(I;p)[i]) | 0≤i≤||full-partition(I;p)|| - 2}| ≤ Σ{|f (a i)|
* (full-partition(I;p)[i + 1] - full-partition(I;p)[i]) | 0≤i≤||full-partition(I;p)|| - 2}

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Latex:

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Latex:
\mforall{}I:Interval
    (icompact(I)
    {}\mRightarrow{}  (\mforall{}f:I  {}\mrightarrow{}\mBbbR{}.  \mforall{}p:partition(I).  \mforall{}y:partition-choice(full-partition(I;p)).
                (|S(f;full-partition(I;p))|  \mleq{}  S(\mlambda{}x.|f  x|;full-partition(I;p)))))


By

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Latex:
(Auto
  THEN  Unfold  `partition-sum`  0
  THEN  Reduce  0
  THEN  (GenConcl  \mkleeneopen{}y  =  a\mkleeneclose{}\mcdot{}  THENA  Auto)
  THEN  (Assert  ||full-partition(I;p)||  =  (||p||  +  2)  BY
                          (Unfold  `full-partition`  0  THEN  Auto')))

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