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


1. A : ℕ ⟶ ℕ ⟶ ℙ@i'
2. B : ℕ ⟶ ℕ ⟶ ℙ@i'
3. ∀n,m:ℕ.  (A[n;m] ⇒ B[n;m])@i
4. b-almost-full(n,m.A[n;m])@i
5. b-almost-full(n,m.B[n;m]) ⇒ b-almost-full(n,m.A[n;m] ∧ B[n;m])
⊢ b-almost-full(n,m.B[n;m])
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{}  \mBbbN{}  {}\mrightarrow{}  \mBbbP{}@i'
2.  B  :  \mBbbN{}  {}\mrightarrow{}  \mBbbN{}  {}\mrightarrow{}  \mBbbP{}@i'
3.  \mforall{}n,m:\mBbbN{}.    (A[n;m]  {}\mRightarrow{}  B[n;m])@i
4.  b-almost-full(n,m.A[n;m])@i
5.  b-almost-full(n,m.B[n;m])  {}\mRightarrow{}  b-almost-full(n,m.A[n;m]  \mwedge{}  B[n;m])
\mvdash{}  b-almost-full(n,m.B[n;m])


By

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

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