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Step * of Lemma sp-lub_wf

∀[A:ℕ ⟶ Sierpinski]. (lub(n.A[n]) ∈ Sierpinski)
BY
{ ((D 0 THENA Auto)
   THEN (InstLemma `quotient-function-subtype` [⌜ℕ⌝;⌜ℕ ⟶ 𝔹⌝;⌜λ2f g.f = ⊥ ∈ (ℕ ⟶ 𝔹) ⇐⇒ g = ⊥ ∈ (ℕ ⟶ 𝔹)⌝]⋅ THENA Auto)
   THEN Fold `Sierpinski` (-1)
   THEN BLemma `sp-lub_wf1`
   THEN SubsumeC ⌜ℕ ⟶ Sierpinski⌝⋅
   THEN Auto) }

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Latex:

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Latex:
\mforall{}[A:\mBbbN{}  {}\mrightarrow{}  Sierpinski].  (lub(n.A[n])  \mmember{}  Sierpinski)


By

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Latex:
((D  0  THENA  Auto)
  THEN  (InstLemma  `quotient-function-subtype`  [\mkleeneopen{}\mBbbN{}\mkleeneclose{};\mkleeneopen{}\mBbbN{}  {}\mrightarrow{}  \mBbbB{}\mkleeneclose{};\mkleeneopen{}\mlambda{}\msubtwo{}f  g.f  =  \mbot{}  \mLeftarrow{}{}\mRightarrow{}  g  =  \mbot{}\mkleeneclose{}]\mcdot{}  THENA  Auto)
  THEN  Fold  `Sierpinski`  (-1)
  THEN  BLemma  `sp-lub\_wf1`
  THEN  SubsumeC  \mkleeneopen{}\mBbbN{}  {}\mrightarrow{}  Sierpinski\mkleeneclose{}\mcdot{}
  THEN  Auto)

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