[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 269 from proof refine-mkdir (previous step)

root[q].dir? ↔ ino1 ∈ dirs, err = err0, root.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-parent(user, q, ROOT_INO, dirs, files), ⌊err0⌋ , psynced → asynced, ino1 ∈ dirs ∨ ino1 ∈ files ⊦ [if err = ESUCCESS then if ¬ inode.directory then err := ENOTDIR else if ¬ px(user, inode.meta) ∨ ¬ pw(user, inode.meta) then err := EACCESS else {dent := negdentry((q + str ').last); afs_lookup#(ino1, dirs, files, asynced; dent, err); if err = ESUCCESS then err := EEXISTS else if err = ENOENT then err := ESUCCESS}; err1 := err; if err1 = ESUCCESS then afs_check_commit#(dirs, files; err1; asynced); fs := abs-files(files); if err1 = ESUCCESS then {dent := negdentry((q + str ').last); afs_mkdir#(md; inode, c_inode, dent, err1, dirs, files; asynced)}] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_mkdir#(q + str ', md, user, fs, abs-of(of); err2, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err1 = err2))

Heuristic symbolic execution applied rule if negative right

And obtained the following new goals

Proof step 270:
root[q].dir? ↔ ino1 ∈ dirs, err = err0, root.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-parent(user, q, ROOT_INO, dirs, files), ⌊err0⌋ , psynced → asynced, ino1 ∈ dirs ∨ ino1 ∈ files ⊦ [skip; err1 := err; if err1 = ESUCCESS then afs_check_commit#(dirs, files; err1; asynced); fs := abs-files(files); if err1 = ESUCCESS then {dent := negdentry((q + str ').last); afs_mkdir#(md; inode, c_inode, dent, err1, dirs, files; asynced)}] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_mkdir#(q + str ', md, user, fs, abs-of(of); err2, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err1 = err2))

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ ⌊err⌋ → err ≠ ESUCCESS; (s)