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Proof step 37 from proof rename-fids (previous step)

root0[path'] = fnode(fid), fnode(fid1) = root0[path], root0[parent(path')].dir?, (root0 -- path)[parent(path')].dir?, fids-cons(root0, fs, ofh), py(user, parent(path'), root0, fs), py(user, parent(path), root0, fs), fid0 ∈ fs, parent(path') ∈ root0, path ∈ root0, path' ∈ root0, fid0 ∈ root0.fids, path' ⊑ path ⊦ fid = fid1, fid0 = fid1, fid0 = fid, path' = ε, path' = path, fid0 ∈ ofh.fids, fid ∈ (root0.fids \ {fid1} ) \ (fnode(fid) -- restn(# path', path)).fids, fid ∈ ofh.fids, fid0 ∈ (root0.fids \ {fid1} ) \ (fnode(fid) -- restn(# path', path)).fids

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, path'] flags: <all paths>

Additional information

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