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Proof step 293 from proof refine-readmeta (previous step)

root.dir?, dom of < ino6, 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-readmeta(path, err1, user, root, abs-files(files), abs-of(of)), ⌊err1⌋

User applied rule case distinction

And obtained the following new goals

Proof step 294:
err1 = EACCESS, root.dir?, dom of < ino6, 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-readmeta(path, err1, user, root, abs-files(files), abs-of(of)), px(user, p', ROOT_INO, dirs, files), ⌊err1⌋
Proof step 301:
⊦ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p ∈ tree ↔ ispath(p, ino, dirs, files))

Rule argument

pos: left 8

Additional information

Used simplifier rules: 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-readmeta(p, ENOENT, user, root, fs, ofh) ↔ ¬ p ∈ root; (s)