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Proof step 6 from proof split-in (previous step)

∀ q, tree. p0 + q ∈ tree ↔ p0 ∈ tree ∧ q ∈ tree[p0] ⊦ (str ' + p0) + q ∈ tree ↔ str ' + p0 ∈ tree ∧ q ∈ tree[str ' + p0]

User applied rule constructor cut

And obtained the following new goals

Proof step 7:
tree = dnode(md, sdt), ∀ q, tree. p0 + q ∈ tree ↔ p0 ∈ tree ∧ q ∈ tree[p0] ⊦ (str ' + p0) + q ∈ tree ↔ str ' + p0 ∈ tree ∧ q ∈ tree[str ' + p0]
Proof step 11:
⊦ ¬ str ' + p ∈ fnode(fid)

Rule argument

var: tree

Additional information

Used simplifier rules: in-fnode: ⊦ ¬ str ' + p ∈ fnode(fid);%directory-tree, entries-tree generated by ∅, dnode, fnode, [ ];;%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]