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Step * 2 of Lemma wfd-tree-cases


1. [A] : Type
2. w : wfd-tree(A)
3. ¬↑co-w-null(w)
⊢ (w = w-nil() ∈ wfd-tree(A)) ∨ ((¬↑co-w-null(w)) ∧ (w = mk-wfd-tree(wfd-subtrees(w)) ∈ wfd-tree(A)))
BY
{ (InstLemma `wfd-subtrees_wf` [⌜A⌝;⌜w⌝]⋅ THENA Auto) }

1
1. [A] : Type
2. w : wfd-tree(A)
3. ¬↑co-w-null(w)
4. wfd-subtrees(w) ∈ A ⟶ wfd-tree(A)
⊢ (w = w-nil() ∈ wfd-tree(A)) ∨ ((¬↑co-w-null(w)) ∧ (w = mk-wfd-tree(wfd-subtrees(w)) ∈ wfd-tree(A)))

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Latex:

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Latex:

1.  [A]  :  Type
2.  w  :  wfd-tree(A)
3.  \mneg{}\muparrow{}co-w-null(w)
\mvdash{}  (w  =  w-nil())  \mvee{}  ((\mneg{}\muparrow{}co-w-null(w))  \mwedge{}  (w  =  mk-wfd-tree(wfd-subtrees(w))))


By

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Latex:
(InstLemma  `wfd-subtrees\_wf`  [\mkleeneopen{}A\mkleeneclose{};\mkleeneopen{}w\mkleeneclose{}]\mcdot{}  THENA  Auto)

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