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Proof step 66 from proof rename-fids (previous step)

root0[path'] = dnode(md0, ∅), dnode(md, sdt) = root0[path], root0[parent(path')].dir?, (root0 -- path)[parent(path')].dir?, fids-cons(root0, fs, ofh), pw(user, path, root0, fs), py(user, parent(path'), root0, fs), py(user, parent(path), root0, fs), parent(path') ∈ root0, path ∈ root0, path' ∈ root0, fid ∈ (root0.fids \ sdt.fids) \ (path' ⊑ path ⊃ dnode(md0, ∅) -- restn(# path', path);dnode(md0, ∅)).fids ∨ fid ∈ sdt.fids ⊦ path' = ε, fid ∈ root0.fids, fid ∈ ofh.fids, fid ∈ fs, path ⊑ path'

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 67:
⊦ ¬ fid ∈ fidb → ¬ fid ∈ fidb \ fidb0
Proof step 68:
root0[path'] = dnode(md0, ∅), dnode(md, sdt) = root0[path], (root0 -- path)[parent(path')].dir?, root0[parent(path')].dir?, fids-cons(root0, fs, ofh), pw(user, path, root0, fs), py(user, parent(path), root0, fs), py(user, parent(path'), root0, fs), path' ∈ root0, path ∈ root0, parent(path') ∈ root0, false ∨ fid ∈ sdt.fids ⊦ path' = ε, fid ∈ fs, fid ∈ ofh.fids, fid ∈ root0.fids, fid ∈ root0.fids \ sdt.fids, path ⊑ path'

Rule argument

spec: bag-union, inst: fidbag name: in-diff-notfirst seq: ⊦ ¬ fid ∈ fidb → ¬ fid ∈ fidb \ fidb0 subst: [fidb0, fidb, fid] → [(path' ⊑ path ⊃ dnode(md0, ∅) -- restn(# path', path) ;dnode(md0, ∅) ) .fids, root0.fids \ sdt.fids, fid] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ¬ fid ∈ fidb → ¬ fid ∈ fidb \ fidb0; (s) Used terms: (path' ⊑ path ⊃ dnode(md0, ∅) -- restn(# path', path);dnode(md0, ∅)) .fids, root0.fids \ sdt.fids, fid