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Proof step 10 from proof split-del (previous step)

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

User applied rule constructor cut

And obtained the following new goals

Proof step 11:
tree = dnode(md, sdt), p0 ∈ tree[str '], str ' ∈ tree, ∀ tree, q. p0 ∈ tree → tree -- (p0 + q) = tree[p0, tree[p0] -- q] ∨ q = ε ⊦ tree -- ((str ' + p0) + q) = tree[str ', tree[str '][p0, tree[str '][p0] -- q]], q = ε
Proof step 17:
⊦ 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, [ ];;