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Proof step 15 from proof inv-truncate (previous step)

root.dir?, fids-cons(root, fs, ofh), pw(user, path, root, fs), path ∈ root ⊦ root[path].dir?, root[path].fid ∈ fs

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: directory-tree name: fnode-elim seq: ¬ tree.dir? ⊦ fid = tree.fid ↔ tree = fnode(fid) subst: [tree, fid] → [root[path], fid]

Additional information

Used simplifier rules: ⊦ p ∈ root ∧ root[p] = fnode(fid) ∧ fids-cons(root, fs, ofh) → fid ∈ fs; (ss)%¬ tree.dir? ⊦ fid = tree.fid ↔ tree = fnode(fid); (elim) Used terms: root[path], fid