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Step * 2 2 2 2 of Lemma sum-partial-has-value


1. n : ℕ
2. m : ℕn
3. f : ℕm ⟶ partial(ℕ)
⊢ istype(∀i:ℕm. (f[i])↓ supposing (Σ(f[x] | x < m))↓)
BY
{ (InstLemma `sum-partial-nat` [⌜m⌝;⌜f⌝]⋅ THEN Auto) }

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Latex:

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Latex:

1.  n  :  \mBbbN{}
2.  m  :  \mBbbN{}n
3.  f  :  \mBbbN{}m  {}\mrightarrow{}  partial(\mBbbN{})
\mvdash{}  istype(\mforall{}i:\mBbbN{}m.  (f[i])\mdownarrow{}  supposing  (\mSigma{}(f[x]  |  x  <  m))\mdownarrow{})


By

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Latex:
(InstLemma  `sum-partial-nat`  [\mkleeneopen{}m\mkleeneclose{};\mkleeneopen{}f\mkleeneclose{}]\mcdot{}  THEN  Auto)

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