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Proof step 225 from proof refine-writemeta (previous step)

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, path, root, abs-files(files)), p' ⊑ parent(path), psynced → asynced ⊦ path = ε, px(user, p', ROOT_INO, dirs, files)

User applied rule insert elim lemma

And obtained the following new goals

Proof step 226:
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)

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