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Proof step 25 from proof refine-unlink (previous step)

err = err0, ino = ROOT_INO, root.dir?, dom of < ino0, 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 ⊦ ∀ ino, err. (∃ q, str. path0 = q + str ' ∧ ( ⌊err⌋ ∨ err = ESUCCESS ∧ ispath(q, ROOT_INO, ino, dirs, files) ∧ px-parent(user, q, ROOT_INO, dirs, files) ∨ err = ENOENT ∧ ¬ ispath(q, ROOT_INO, dirs, files) ∨ err = EACCESS ∧ (∃ p'. p' ⊑ q ∧ ispath(p', ROOT_INO, dirs, files) ∧ ¬ px(user, p', ROOT_INO, dirs, files)))) → [dent := negdentry(path0.last); if err = ESUCCESS then {isdir := false; vfs_may_delete_check#(ino, user, dirs, files, asynced; inode, isdir, dent, p_inode, err)}; if err = ESUCCESS then afs_check_commit#(dirs, files; err; asynced); fs := abs-files(files); if err = ESUCCESS then {afs_unlink#(; inode, p_inode, dent, err, dirs, files; asynced); vfs_put_inode#(p_inode, of, asynced; err, dirs, files)}] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_unlink#(path0, user, abs-of(of); err0, root, fs; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err0)), path0 = ε

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 26:
root.dir?, dom of < ino0, 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⌋ ∨ err1 = ESUCCESS ∧ ispath(q, ROOT_INO, ino1, dirs, files) ∧ px-parent(user, q, ROOT_INO, dirs, files) ∨ err1 = ENOENT ∧ ¬ ispath(q, ROOT_INO, dirs, files) ∨ err1 = EACCESS ∧ p' ⊑ q ∧ ispath(p', ROOT_INO, dirs, files) ∧ ¬ px(user, p', ROOT_INO, dirs, files) ⊦ [dent := negdentry((q + str ').last); if err1 = ESUCCESS then {isdir := false; vfs_may_delete_check#(ino1, user, dirs, files, asynced; inode, isdir, dent, p_inode, err1)}; if err1 = ESUCCESS then afs_check_commit#(dirs, files; err1; asynced); fs := abs-files(files); if err1 = ESUCCESS then {afs_unlink#(; inode, p_inode, dent, err1, dirs, files; asynced); vfs_put_inode#(p_inode, of, asynced; err1, dirs, files)}] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_unlink#(q + str ', user, abs-of(of); err0, root, fs; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err1 = err0))

Rule argument

Additional information

Used simplifier rules: a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]% ⊦ p + str ' ≠ ε; (s)