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Proof step 13 from proof inv-open (previous step)

fid ∈ fs ↔ fid ∈ root.fids ∨ fid ∈ ofh.fids, root.dir?, fids-cons(root, fs, ofh), path ∈ root, mode = MODE_R ∨ mode = MODE_RW → pr(user, path, root, fs), mode = MODE_W ∨ mode = MODE_RW → pw(user, path, root, fs) ⊦ fid ∈ fs ↔ fid ∈ root.fids ∨ fid = root[path].fid ∨ fid ∈ ofh.fids, root[path].dir?, n ∈ ofh

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 14:
fid ∈ fs ↔ fid ∈ root.fids ∨ fid ∈ ofh.fids, root[path] = fnode(fid0), root.dir?, fids-cons(root, fs, ofh), path ∈ root, mode = MODE_W ∨ mode = MODE_RW → pw(user, path, root, fs), mode = MODE_R ∨ mode = MODE_RW → pr(user, path, root, fs) ⊦ fid ∈ fs ↔ fid ∈ root.fids ∨ fid = fid0 ∨ fid ∈ ofh.fids, root[path].dir?, n ∈ ofh

Rule argument

spec: directory-tree name: fnode-elim seq: ¬ tree.dir? ⊦ fid = tree.fid ↔ tree = fnode(fid) subst: [tree, fid] → [root[path], fid0]

Additional information

Used simplifier rules: ¬ tree.dir? ⊦ fid = tree.fid ↔ tree = fnode(fid); (elim) Used terms: root[path], fid0