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


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

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Latex:

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Latex:

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


By

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Latex:
(UseWitness  \mkleeneopen{}ɘ,  1,  Ax>\mkleeneclose{}\mcdot{}  THEN  MemTypeCD  THEN  Auto)

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