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Proof step 4 from proof put-fnode (previous step)

tree[p, tree0] = fnode(fid), p ∈ tree ⊦ p = ε ∧ tree0 = fnode(fid)

User applied rule constructor cut

And obtained the following new goals

Proof step 5:
tree[p, tree0] = fnode(fid), tree = dnode(md, sdt), p ∈ tree ⊦ p = ε ∧ tree0 = fnode(fid)
Proof step 14:
⊦ p ∈ fnode(fid) ↔ p = ε
Proof step 15:
⊦ tree[ε, tree0] = tree0

Rule argument

var: tree

Additional information

Used simplifier rules: fnode-notin: ⊦ p ∈ fnode(fid) ↔ p = ε;%nil-put: ⊦ tree[ε, tree0] = tree0;%directory-tree, entries-tree generated by ∅, dnode, fnode, [ ];;