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Step * 2 1 1 of Lemma wfd-tree-cases


1. A : Type
2. w : wfd-tree(A)
3. ¬↑co-w-null(w)
4. wfd-subtrees(w) ∈ A ⟶ wfd-tree(A)
5. ¬↑co-w-null(w)
⊢ w = mk-wfd-tree(wfd-subtrees(w)) ∈ wfd-tree(A)
BY
{ xxxSubst' mk-wfd-tree(wfd-subtrees(w)) ~ w 0xxx }

1
.....equality..... 
1. A : Type
2. w : wfd-tree(A)
3. ¬↑co-w-null(w)
4. wfd-subtrees(w) ∈ A ⟶ wfd-tree(A)
5. ¬↑co-w-null(w)
⊢ mk-wfd-tree(wfd-subtrees(w)) ~ w

2
1. A : Type
2. w : wfd-tree(A)
3. ¬↑co-w-null(w)
4. wfd-subtrees(w) ∈ A ⟶ wfd-tree(A)
5. ¬↑co-w-null(w)
⊢ w = 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)
4.  wfd-subtrees(w)  \mmember{}  A  {}\mrightarrow{}  wfd-tree(A)
5.  \mneg{}\muparrow{}co-w-null(w)
\mvdash{}  w  =  mk-wfd-tree(wfd-subtrees(w))


By

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Latex:
xxxSubst'  mk-wfd-tree(wfd-subtrees(w))  \msim{}  w  0xxx

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