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Step * 3 1 of Lemma u-almost-full-filter


1. A : ℕ ⟶ ℙ@i'
2. B : ℕ ⟶ ℙ@i'
3. u-almost-full(n.A[n]) ⇒ u-almost-full(n.B[n]) ⇒ u-almost-full(n.A[n] ∧ B[n])
4. (∀n:ℕ. (A[n] ⇒ B[n])) ⇒ u-almost-full(n.A[n]) ⇒ u-almost-full(n.B[n])
5. s : StrictInc@i
⊢ ⇃(∃n:ℕ. True)
BY
{ (UseWitness ⌜<0, Ax>⌝⋅ THEN MemTypeCD THEN Auto) }

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Latex:

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Latex:

1.  A  :  \mBbbN{}  {}\mrightarrow{}  \mBbbP{}@i'
2.  B  :  \mBbbN{}  {}\mrightarrow{}  \mBbbP{}@i'
3.  u-almost-full(n.A[n])  {}\mRightarrow{}  u-almost-full(n.B[n])  {}\mRightarrow{}  u-almost-full(n.A[n]  \mwedge{}  B[n])
4.  (\mforall{}n:\mBbbN{}.  (A[n]  {}\mRightarrow{}  B[n]))  {}\mRightarrow{}  u-almost-full(n.A[n])  {}\mRightarrow{}  u-almost-full(n.B[n])
5.  s  :  StrictInc@i
\mvdash{}  \00D9(\mexists{}n:\mBbbN{}.  True)


By

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Latex:
(UseWitness  \mkleeneopen{}ɘ,  Ax>\mkleeneclose{}\mcdot{}  THEN  MemTypeCD  THEN  Auto)

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