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Proof step 6 from proof fids-put1 (previous step)

tree0[parent(str ' + p0)].dir?, str ' ∈ tree0, p0 ∈ tree0[str '], ∀ tree0, tree1. tree0[parent(p0)].dir? ∧ p0 ∈ tree0 → tree0[p0, tree1].fids = (tree0.fids ∪ tree1.fids) \ tree0[p0].fids ∨ p0 = ε ⊦ tree0[str ' + p0, tree1].fids = (tree0.fids ∪ tree1.fids) \ tree0[str ' + p0].fids

User applied rule constructor cut

And obtained the following new goals

Proof step 7:
tree0 = dnode(md, sdt), tree0[parent(str ' + p0)].dir?, p0 ∈ tree0[str '], str ' ∈ tree0, ∀ tree0, tree1. tree0[parent(p0)].dir? ∧ p0 ∈ tree0 → tree0[p0, tree1].fids = (tree0.fids ∪ tree1.fids) \ tree0[p0].fids ∨ p0 = ε ⊦ tree0[str ' + p0, tree1].fids = (tree0.fids ∪ tree1.fids) \ tree0[str ' + p0].fids
Proof step 42:
⊦ fnode(fid).fids = {fid}

Rule argument

var: tree0

Additional information

Used simplifier rules: fids-fnode: ⊦ fnode(fid).fids = {fid} ;%directory-tree, entries-tree generated by ∅, dnode, fnode, [ ];;% ⊦ str ' ∈ fnode(fid) ↔ false; (s)