---

Step * 3 1 of Lemma nwkl!-iff-twkl!-bool


1. ∀A:{A:(𝔹 List) ⟶ ℙ| down-closed(𝔹;A) ∧ Unbounded(A)} 
     (Decidable(A) ⇒ eff-unique-path(𝔹;A) ⇒ (∃f:{ℕ ⟶ 𝔹| is-path(A;f)}))
2. A : (𝔹 List) ⟶ ℙ
3. Decidable(A)
4. infinite-tree(A)
5. eff-unique-path(𝔹;A)
6. f : ℕ ⟶ 𝔹
7. [%9] : is-path(A;f)
⊢ SqStable(is-path(A;f))
BY
{ (RepUR ``dec-predicate`` 3 THEN Unfold `is-path` 0 THEN Auto) }

---

Latex:

---

Latex:

1.  \mforall{}A:\{A:(\mBbbB{}  List)  {}\mrightarrow{}  \mBbbP{}|  down-closed(\mBbbB{};A)  \mwedge{}  Unbounded(A)\} 
          (Decidable(A)  {}\mRightarrow{}  eff-unique-path(\mBbbB{};A)  {}\mRightarrow{}  (\mexists{}f:\{\mBbbN{}  {}\mrightarrow{}  \mBbbB{}|  is-path(A;f)\}))
2.  A  :  (\mBbbB{}  List)  {}\mrightarrow{}  \mBbbP{}
3.  Decidable(A)
4.  infinite-tree(A)
5.  eff-unique-path(\mBbbB{};A)
6.  f  :  \mBbbN{}  {}\mrightarrow{}  \mBbbB{}
7.  [\%9]  :  is-path(A;f)
\mvdash{}  SqStable(is-path(A;f))


By

---

Latex:
(RepUR  ``dec-predicate``  3  THEN  Unfold  `is-path`  0  THEN  Auto)

---

Home Index