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Proof step 226 from proof refine-writemeta (previous step)

root[p'].dir? ↔ m ∈ dirs, path = q + str ', root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(p', ROOT_INO, m, dirs, files), of-cons(of, dirs, files), pw(user, path, root, abs-files(files)), p' ⊑ q, psynced → asynced ⊦ path = ε, px(user, p', ROOT_INO, dirs, files)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 227:
root[p'].dir? ↔ m ∈ dirs, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(p', ROOT_INO, m, dirs, files), of-cons(of, dirs, files), pw(user, q + str ', root, abs-files(files)), p' ⊑ q, psynced → asynced ⊦ px(user, p', ROOT_INO, dirs, files)

Rule argument

Additional information

Used simplifier rules: a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]% ⊦ p + str ' ≠ ε; (s)