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Proof step 511 from proof refine-link (previous step)

dirs[ino1] = mkdir(# entries0, md0, # links(ino1, dirs), m2, entries0), root.dir?, root[q].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), entries0[str] ∈ files, ino1 ∈ dirs, str ∈ entries0, psynced → asynced, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO, err1 = EACCESS ∧ p' ⊑ q0 ∧ ispath(p', ROOT_INO, dirs, files) ∧ ¬ px(user, p', ROOT_INO, dirs, files) ∨ err1 = ENOENT ∧ ¬ ispath(q0, ROOT_INO, dirs, files) ⊦ err1 = ESUCCESS, root[q + str '].dir?, pre-link(q + str ', q0 + str0 ', err1, user, root, abs-files(files), abs-of(of)), entries0[str] ∈ dirs, ⌊err1⌋

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: left 17

Additional information

Used simplifier rules: ispath-target: ⊦ ispath(p, ino, dirs, files) ↔ (∃ m. ispath(p, ino, m, dirs, files));%px: ⊦ ispath(p, ino, m, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → ( px(user, p, tree, abs-files(files)) ↔ px(user, p, ino, dirs, files));%py-prefix: ⊦ ispath(q, ino, m, dirs, files) ∧ py(user, p, tree, abs-files(files)) ∧ q ⊑ p ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → px(user, q, ino, dirs, files);%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));% ⊦ ESUCCESS ≠ ENOENT; (s)% ⊦ ¬ ⌊ENOENT⌋ ; (s)%⊦ pre-link(p, p', ENOENT, user, root, fs, ofh) ↔ ¬ p ∈ root ∨ ¬ parent(p') ∈ root; (s)% ⊦ p + q ∈ tree ↔ p ∈ tree ∧ q ∈ tree[p]; (s)% ⊦ ispath(p, n, m, dirs, files) → ispath(p, n, dirs, files); (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]% ⊦ parent(p + str ') = p; (s)% ⊦ ESUCCESS ≠ EACCESS; (s)% ⊦ ¬ ⌊EACCESS⌋ ; (s)%⊦ pre-link(p, p', EACCESS, user, root, fs, ofh) ↔ ¬ px(user, parent(p), root, fs) ∨ ¬ py(user, parent(p'), root, fs); (s)%⊦ px(user, p, ino, dirs, files) → px-parent(user, p, ino, dirs, files); (s)