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Step * 1 of Lemma ni-min-zero


1. x : ℕ∞
2. ni-min(x;0∞) = ni-min(x;0∞) ∈ (ℕ ⟶ 𝔹)
⊢ ni-min(x;0∞) = 0∞ ∈ (ℕ ⟶ 𝔹)
BY
{ (Ext⋅ THEN Auto THEN RenameVar `i' (-1) THEN RepUR ``ni-min nat-inf-infinity nat2inf`` 0 THEN AutoBoolCase ⌜x i⌝⋅) }

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Latex:

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Latex:

1.  x  :  \mBbbN{}\minfty{}
2.  ni-min(x;0\minfty{})  =  ni-min(x;0\minfty{})
\mvdash{}  ni-min(x;0\minfty{})  =  0\minfty{}


By

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Latex:
(Ext\mcdot{}
  THEN  Auto
  THEN  RenameVar  `i'  (-1)
  THEN  RepUR  ``ni-min  nat-inf-infinity  nat2inf``  0
  THEN  AutoBoolCase  \mkleeneopen{}x  i\mkleeneclose{}\mcdot{})

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