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Proof step 3 from proof refine-writemeta (previous step)

err = err0, fs = abs-files(files), root.dir?, dom of < ino, 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 ⊦ ⟪vfs_writemeta#(path, md, user; err, dirs, files, asynced)⟫ ⟨posix_writemeta#(path, md, user, abs-of(of); err0, root, fs; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err0)

User applied rule call right

And obtained the following new goals

Proof step 4:
err = err0, fs = abs-files(files), root.dir?, dom of < ino, 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 ⊦ ⟪let ino = ROOT_INO in {vfs_walk#(path, user, dirs, files, asynced; ino, err); if err = ESUCCESS then choose inode with true in {afs_iget#(ino, dirs, files, asynced; inode, err); if err = ESUCCESS then if pw(user, inode.meta) then {inode.meta := md; afs_check_commit#(dirs, files; err; asynced); if err = ESUCCESS then afs_write_inode#(inode; err, dirs, files; asynced)} else err := EACCESS}}⟫ ⟨posix_writemeta#(path, md, user, abs-of(of); err0, root, fs; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err0)

Rule argument

pos: right 1

Additional information

Used simplifier rules: vfs_writemeta#(PATH, MD, USER; ERR, DIRS, FILES, ASYNCED) {let INO = ROOT_INO in {vfs_walk#(PATH, USER, DIRS, FILES, ASYNCED; INO, ERR); if ERR = ESUCCESS then choose INODE with true in {afs_iget#(INO, DIRS, FILES, ASYNCED; INODE, ERR); if ERR = ESUCCESS then if pw(USER, INODE.meta) then {INODE.meta := MD; afs_check_commit#(DIRS, FILES; ERR; ASYNCED); if ERR = ESUCCESS then afs_write_inode# (INODE; ERR, DIRS, FILES; ASYNCED)} else ERR := EACCESS}} };