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Proof step 5 from proof fids-del (previous step)

str ' ∈ tree, p0 ∈ tree[str '], ∀ tree. p0 ∈ tree → (tree -- p0).fids = tree.fids \ tree[p0].fids ∨ p0 = ε ⊦ (tree -- (str ' + p0)).fids = tree.fids \ tree[str ' + p0].fids

User applied rule constructor cut

And obtained the following new goals

Proof step 6:
tree = dnode(md, sdt), p0 ∈ tree[str '], str ' ∈ tree, ∀ tree. p0 ∈ tree → (tree -- p0).fids = tree.fids \ tree[p0].fids ∨ p0 = ε ⊦ (tree -- (str ' + p0)).fids = tree.fids \ tree[str ' + p0].fids
Proof step 22:
⊦ fnode(fid).fids = {fid}

Rule argument

var: tree

Additional information

Used simplifier rules: fids-fnode: ⊦ fnode(fid).fids = {fid} ;%directory-tree, entries-tree generated by ∅, dnode, fnode, [ ];;% ⊦ str ' ∈ fnode(fid) ↔ false; (s)