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Proof step 221 from proof refine-writemeta (previous step)

err1 = EACCESS, 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, dirs, files), of-cons(of, dirs, files), p' ⊑ parent(path), psynced → asynced ⊦ err1 = ESUCCESS, path = ε, pre-writemeta(path, md, err1, user, root, abs-files(files), abs-of(of)), px(user, p', ROOT_INO, dirs, files), ⌊err1⌋

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 222:
⊦ ispath(p, ino, dirs, files) ↔ (∃ m. ispath(p, ino, m, dirs, files))
Proof step 223:
⊦ ispath(p, ino, m, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → p ∈ tree ∧ (tree[p].dir? ↔ m ∈ dirs)
Proof step 224:
⊦ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p ∈ tree ↔ ispath(p, ino, dirs, files))
Proof step 225:
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)

Rule argument

Additional information

Used simplifier rules: ispath-target: ⊦ ispath(p, ino, dirs, files) ↔ (∃ m. ispath(p, ino, m, dirs, files));%path-in: ⊦ ispath(p, ino, m, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → p ∈ tree ∧ (tree[p].dir? ↔ m ∈ dirs);%path-in-eq: ⊦ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p ∈ tree ↔ ispath(p, ino, dirs, files));% ⊦ ispath(p, n, m, dirs, files) → ispath(p, n, dirs, files); (s)%⊦ pre-writemeta(p, md, EACCESS, user, root, fs, ofh) ↔ ¬ pw(user, p, root, fs); (s)% ⊦ ¬ ⌊EACCESS⌋ ; (s)% ⊦ ESUCCESS ≠ EACCESS; (s)