[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 10 from proof inv-fsync (previous step)

err = ESUCCESS, ino = ROOT_INO, afs-cons(dirs, files), of-cons(of, dirs, files) ⊦ [vfs_walk#(p, user, dirs, files, asynced; ino, err)] ( ⌊err⌋ ∨ err = ESUCCESS ∧ ispath(p, ROOT_INO, ino, dirs, files) ∧ px-parent(user, p, ROOT_INO, dirs, files) ∨ err = ENOENT ∧ ¬ ispath(p, ROOT_INO, dirs, files) ∨ err = EACCESS ∧ p ≠ ε ∧ (∃ p'. p' ⊑ parent(p) ∧ ispath(p', ROOT_INO, dirs, files) ∧ ¬ px(user, p', ROOT_INO, dirs, files)) → ⟪if err = ESUCCESS then let isdir = false in vfs_may_open#(ino, isdir, MODE_R, user, dirs, files, asynced; inode, err); if err = ESUCCESS then afs_fsync#(inode, isdir0, dirs, files; ; asynced, err); if err = ESUCCESS then afs_sync#(dirs, files; ; asynced, err)⟫ true)

User applied rule split right

And obtained the following new goals

Proof step 11:
⟨vfs_walk#(p, user, dirs, files, asynced; ino, err)⟩ (ino = ino0 ∧ err = err0), err = ESUCCESS, ino = ROOT_INO, afs-cons(dirs, files), of-cons(of, dirs, files), ⌊err0⌋ ∨ err0 = ESUCCESS ∧ ispath(p, ROOT_INO, ino0, dirs, files) ∧ px-parent(user, p, ROOT_INO, dirs, files) ∨ err0 = ENOENT ∧ ¬ ispath(p, ROOT_INO, dirs, files) ∨ err0 = EACCESS ∧ p ≠ ε ∧ (∃ p'. p' ⊑ parent(p) ∧ ispath(p', ROOT_INO, dirs, files) ∧ ¬ px(user, p', ROOT_INO, dirs, files)) ⊦ ⟪if err0 = ESUCCESS then let isdir = false in vfs_may_open#(ino0, isdir, MODE_R, user, dirs, files, asynced; inode, err0); if err0 = ESUCCESS then afs_fsync#(inode, isdir0, dirs, files; ; asynced, err0); if err0 = ESUCCESS then afs_sync#(dirs, files; ; asynced, err0)⟫ true

Rule argument

pos: right 1

Proof step 10 from proof inv-fsync (previous step)

User applied rule split right

And obtained the following new goals

Rule argument

Additional information