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Proof step 107 from proof rename-fids (previous step)

fid ∈ fs ↔ fid ∈ root0.fids ∨ fid ∈ ofh.fids, root0[p0].dir?, fids-cons(root0, fs, ofh), py(user, p0, root0, fs), py(user, parent(path), root0, fs), p0 ∈ root0, path ∈ root0, p0 ⊑ path, root0[path].dir? → pw(user, path, root0, fs) ⊦ fid ∈ fs ↔ fid ∈ (root0 -- path)[p0 + str ', root0[path]].fids ∨ fid ∈ ofh.fids, (root0[p0] -- restn(# p0, path)).dir?, str ' ∈ root0[p0], path ⊑ p0 + str '

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: list-last, inst: path name: prefix seq: ⊦ p ⊑ p0 ↔ (∃ p1. p + p1 = p0) subst: [p0, p] → [path, p0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ p + q ∈ tree ↔ p ∈ tree ∧ q ∈ tree[p]; (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]% ⊦ p + p0 ⊑ p + p1 ↔ p0 ⊑ p1; (s)% ⊦ p ⊑ str ' ↔ p = ε ∨ p = str '; (s)% ⊦ p ≠ ε → parent(p0 + p) = p0 + parent(p); (s)% ⊦ restn(# p, p + p0) = p0; (s)%p ≠ ε ⊦ p ∈ tree → ((tree -- p).dir? ↔ tree.dir?); (s) Used terms: path, p0