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Step * 2 of Lemma u-almost-full-filter


1. A : ℕ ⟶ ℙ@i'
2. B : ℕ ⟶ ℙ@i'
3. ∀n:ℕ. (A[n] ⇒ B[n])@i
4. u-almost-full(n.A[n])@i
5. u-almost-full(n.B[n]) ⇒ u-almost-full(n.A[n] ∧ B[n])
⊢ u-almost-full(n.B[n])
BY
{ (RepeatFor 2 (ParallelOp -2) THEN MoveToConcl (-1) THEN BLemma `implies-quotient-true` 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.  \mforall{}n:\mBbbN{}.  (A[n]  {}\mRightarrow{}  B[n])@i
4.  u-almost-full(n.A[n])@i
5.  u-almost-full(n.B[n])  {}\mRightarrow{}  u-almost-full(n.A[n]  \mwedge{}  B[n])
\mvdash{}  u-almost-full(n.B[n])


By

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Latex:
(RepeatFor  2  (ParallelOp  -2)  THEN  MoveToConcl  (-1)  THEN  BLemma  `implies-quotient-true`  THEN  Auto)

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