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


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

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Latex:

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Latex:

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


By

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Latex:
(RepUR  ``dec-predicate``  4  THEN  Unfold  `infinite-tree`  0  THEN  Auto)

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