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Step * of Lemma isEven-sum

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∀[n:ℕ]. ∀[f:ℕn ⟶ ℤ].  uiff(↑isEven(Σ(f[x] | x < n));↑isEven(||filter(λx.isOdd(f[x]);upto(n))||))
BY
{ (Intros THEN (RWO "even-iff-not-odd" 0 THENA Auto) THEN RWO  "isOdd-sum" 0 THEN Auto) }

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Latex:

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Latex:
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\mforall{}[n:\mBbbN{}].  \mforall{}[f:\mBbbN{}n  {}\mrightarrow{}  \mBbbZ{}].    uiff(\muparrow{}isEven(\mSigma{}(f[x]  |  x  <  n));\muparrow{}isEven(||filter(\mlambda{}x.isOdd(f[x]);upto(n))||))


By

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Latex:
(Intros  THEN  (RWO  "even-iff-not-odd"  0  THENA  Auto)  THEN  RWO    "isOdd-sum"  0  THEN  Auto)

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