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Proof step 19 from proof rename-fids (previous step)

fid0 ∈ fs ↔ fid0 ∈ root0.fids ∨ fid0 ∈ ofh.fids, root0[path'] = fnode(fid), root0[parent(path')].dir?, fids-cons(root0, fs, ofh), py(user, parent(path), root0, fs), py(user, parent(path'), root0, fs), path' ∈ root0, path ∈ root0, parent(path') ∈ root0 ⊦ fid0 ≠ fid ∧ fid0 ∈ fs ↔ fid0 ∈ (root0 -- path)[path', root0[path]].fids ∨ fid0 ∈ ofh.fids, path' = ε, root0[path].dir?, (root0 -- path)[parent(path')].dir?, fid ∈ ofh.fids, fid ∈ (root0 -- path)[path', root0[path]].fids, path ⊑ path'

User applied rule insert elim lemma

And obtained the following new goals

Proof step 20:
fid0 ∈ fs ↔ fid0 ∈ root0.fids ∨ fid0 ∈ ofh.fids, root0[path'] = fnode(fid), path' = q + str ', root0[q].dir?, fids-cons(root0, fs, ofh), py(user, q, root0, fs), py(user, parent(path), root0, fs), q ∈ root0, path ∈ root0, path' ∈ root0 ⊦ fid0 ≠ fid ∧ fid0 ∈ fs ↔ fid0 ∈ (root0 -- path)[path', root0[path]].fids ∨ fid0 ∈ ofh.fids, path' = ε, (root0 -- path)[q].dir?, root0[path].dir?, fid ∈ (root0 -- path)[path', root0[path]].fids, fid ∈ ofh.fids, path ⊑ path'

Rule argument

spec: path name: parent-elim seq: p ≠ ε ⊦ q = parent(p) ∧ str = p.last ↔ p = q + str ' subst: [p, q, str] → [path', q, str]

Additional information

Used simplifier rules: p ≠ ε ⊦ q = parent(p) ∧ str = p.last ↔ p = q + str '; (elim) Used terms: path', q, str