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Proof step 10 from proof same-in (previous step)

str ' ∈ tree, p0 ∈ tree[str '], ∀ tree, tree0. p0 ∈ tree → p0 ∈ tree[p0, tree0] ⊦ str ' ∈ tree[str ', tree[str '][p0, tree0]] ∧ p0 ∈ tree[str '][p0, tree0]

User applied rule constructor cut

And obtained the following new goals

Proof step 11:
tree = dnode(md, sdt), p0 ∈ tree[str '], str ' ∈ tree, ∀ tree, tree0. p0 ∈ tree → p0 ∈ tree[p0, tree0] ⊦ str ' ∈ tree[str ', tree[str '][p0, tree0]] ∧ p0 ∈ tree[str '][p0, tree0]
Proof step 16:
⊦ str ' ∈ fnode(fid) ↔ false

Rule argument

var: tree

Additional information

Used simplifier rules: one-inf: ⊦ str ' ∈ fnode(fid) ↔ false;%directory-tree, entries-tree generated by ∅, dnode, fnode, [ ];;