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Proof step 134 from proof refine-open (previous step)

root.dir?, dom of < ino2, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), of-cons(of, dirs, files), psynced → asynced, err1 = EACCESS ∧ path ≠ ε ∧ p' ⊑ parent(path) ∧ ispath(p', ROOT_INO, dirs, files) ∧ ¬ px(user, p', ROOT_INO, dirs, files) ∨ err1 = ENOENT ∧ ¬ ispath(path, ROOT_INO, dirs, files) ⊦ err1 = ESUCCESS, pre-open(path, mode, err1, user, root, abs-files(files), abs-of(of)), ⌊err1⌋

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: left 8

Additional information

Used simplifier rules: ispath-target: ⊦ ispath(p, ino, dirs, files) ↔ (∃ m. ispath(p, ino, m, dirs, files));%px-prefix: ⊦ ispath(q, ino, m, dirs, files) ∧ px(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-open(p, mode, ENOENT, user, root, fs, ofh) ↔ ¬ p ∈ root; (s)% ⊦ ESUCCESS ≠ EACCESS; (s)% ⊦ ¬ ⌊EACCESS⌋ ; (s)%⊦ pre-open(p, mode, EACCESS, user, root, fs, ofh) ↔ (mode = MODE_R ∨ mode = MODE_RW) ∧ ¬ pr(user, p, root, fs) ∨ (mode = MODE_W ∨ mode = MODE_RW) ∧ ¬ pw(user, p, root, fs) ∨ ¬ px(user, parent(p), root, fs); (s)