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Step * 1 1 1 of Lemma int_lower_well_founded


1. n : ℤ
2. WellFnd{i}(ℕ;x,y.x < y)
3. WellFnd{i}({...n};x,y.(λz.(n - z)) x < (λz.(n - z)) y)
⊢ WellFnd{i}({...n};x,y.x > y)
BY
{ Reduce 3 }

1
1. n : ℤ
2. WellFnd{i}(ℕ;x,y.x < y)
3. WellFnd{i}({...n};x,y.n - x < n - y)
⊢ WellFnd{i}({...n};x,y.x > y)

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Latex:

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Latex:

1.  n  :  \mBbbZ{}
2.  WellFnd\{i\}(\mBbbN{};x,y.x  <  y)
3.  WellFnd\{i\}(\{...n\};x,y.(\mlambda{}z.(n  -  z))  x  <  (\mlambda{}z.(n  -  z))  y)
\mvdash{}  WellFnd\{i\}(\{...n\};x,y.x  >  y)


By

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Latex:
Reduce  3

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