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Step * 1 1 1 of Lemma int_seg_well_founded_down


1. i : ℤ
2. j : {i...}
3. WellFnd{i}({0...};x,y.x < y)
4. WellFnd{i}({i..j-};x,y.(λx.(j - x)) x < (λx.(j - x)) y)
⊢ WellFnd{i}({i..j-};x,y.x > y)
BY
{ Reduce 4 }

1
1. i : ℤ
2. j : {i...}
3. WellFnd{i}({0...};x,y.x < y)
4. WellFnd{i}({i..j-};x,y.j - x < j - y)
⊢ WellFnd{i}({i..j-};x,y.x > y)

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Latex:

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Latex:

1.  i  :  \mBbbZ{}
2.  j  :  \{i...\}
3.  WellFnd\{i\}(\{0...\};x,y.x  <  y)
4.  WellFnd\{i\}(\{i..j\msupminus{}\};x,y.(\mlambda{}x.(j  -  x))  x  <  (\mlambda{}x.(j  -  x))  y)
\mvdash{}  WellFnd\{i\}(\{i..j\msupminus{}\};x,y.x  >  y)


By

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Latex:
Reduce  4

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