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Step * 1 1 1 of Lemma int_upper_well_founded


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

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

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Latex:

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Latex:

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


By

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Latex:
Reduce  3

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