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Proof step 6 from proof fids-put3 (previous step)

tree[str ' + p0] = dnode(md0, sdt), str ' ∈ tree, p0 ∈ tree[str '], ∀ tree, md0, sdt, md1. tree[p0] = dnode(md0, sdt) ∧ p0 ∈ tree → tree[p0, dnode(md1, sdt)].fids = tree.fids ⊦ tree[str ' + p0, dnode(md1, sdt)].fids = tree.fids

User applied rule constructor cut

And obtained the following new goals

Proof step 7:
tree[str ' + p0] = dnode(md0, sdt), tree = dnode(md, sdt0), p0 ∈ tree[str '], str ' ∈ tree, ∀ tree, md0, sdt, md1. tree[p0] = dnode(md0, sdt) ∧ p0 ∈ tree → tree[p0, dnode(md1, sdt)].fids = tree.fids ⊦ tree[str ' + p0, dnode(md1, sdt)].fids = tree.fids
Proof step 21:
⊦ fnode(fid).fids = {fid}

Rule argument

var: tree

Additional information

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