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Proof step 9 from proof split-put (previous step)

str ' ∈ tree, p0 ∈ tree[str '], ∀ tree, q, tree0. p0 ∈ tree → tree[p0 + q, tree0] = tree[p0, tree[p0][q, tree0]] ⊦ tree[(str ' + p0) + q, tree0] = tree[str ' + p0, tree[str '][p0][q, tree0]]

User applied rule constructor cut

And obtained the following new goals

Proof step 10:
tree = dnode(md, sdt), p0 ∈ tree[str '], str ' ∈ tree, ∀ tree, q, tree0. p0 ∈ tree → tree[p0 + q, tree0] = tree[p0, tree[p0][q, tree0]] ⊦ tree[(str ' + p0) + q, tree0] = tree[str ' + p0, tree[str '][p0][q, tree0]]
Proof step 27:
⊦ 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, [ ];;