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Step * 1 1 of Lemma assert-co-w-null


1. A : Type
2. w : co-w(A)
3. co-w(A) ≡ Unit + (A ⟶ co-w(A))
⊢ (↑co-w-null(w)) ⇒ (w = w-nil() ∈ wfd-tree(A))
BY
{ (GenConcl ⌜w = z ∈ (Unit + (A ⟶ co-w(A)))⌝⋅ THENA Auto) }

1
1. A : Type
2. w : co-w(A)
3. co-w(A) ≡ Unit + (A ⟶ co-w(A))
4. z : Unit + (A ⟶ co-w(A))
5. w = z ∈ (Unit + (A ⟶ co-w(A)))
⊢ (↑co-w-null(z)) ⇒ (z = w-nil() ∈ wfd-tree(A))

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Latex:

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Latex:

1.  A  :  Type
2.  w  :  co-w(A)
3.  co-w(A)  \mequiv{}  Unit  +  (A  {}\mrightarrow{}  co-w(A))
\mvdash{}  (\muparrow{}co-w-null(w))  {}\mRightarrow{}  (w  =  w-nil())


By

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Latex:
(GenConcl  \mkleeneopen{}w  =  z\mkleeneclose{}\mcdot{}  THENA  Auto)

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