---

Step * 3 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])
⊢ b-almost-full(n,m.True)
BY
{ (D 0 THEN Auto) }

1
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)

---

Latex:

---

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])
\mvdash{}  b-almost-full(n,m.True)


By

---

Latex:
(D  0  THEN  Auto)

---

Home Index