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Step * 1 of Lemma int_upper_ind_uniform


1. i : ℤ@i
2. [E] : {i...} ⟶ ℙ{u}
3. ∀[k:{i...}]. ((∀[j:{i..k-}]. E[j]) ⇒ E[k])@[u | i]
⊢ ∀[k:{i...}]. E[k]
BY
{ ((InstLemma `int_upper_uwell_founded` [⌜parm{u}⌝;⌜i⌝]⋅ THENA Auto)
   THEN Unfold `uwellfounded` -1
   THEN InstHyp [⌜E⌝] (-1)⋅
   THEN Auto) }

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Latex:

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Latex:

1.  i  :  \mBbbZ{}@i
2.  [E]  :  \{i...\}  {}\mrightarrow{}  \mBbbP{}\{u\}
3.  \mforall{}[k:\{i...\}].  ((\mforall{}[j:\{i..k\msupminus{}\}].  E[j])  {}\mRightarrow{}  E[k])@[u  |  i]
\mvdash{}  \mforall{}[k:\{i...\}].  E[k]


By

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Latex:
((InstLemma  `int\_upper\_uwell\_founded`  [\mkleeneopen{}parm\{u\}\mkleeneclose{};\mkleeneopen{}i\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  Unfold  `uwellfounded`  -1
  THEN  InstHyp  [\mkleeneopen{}E\mkleeneclose{}]  (-1)\mcdot{}
  THEN  Auto)

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