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Proof step 6 from proof refine-fsync (previous step)

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_fsync#(path, isdir, user, dirs, files; asynced; err)] ⟨posix_fsync#(path, isdir, user, root, abs-files(files), abs-of(of); ; psynced, err0)⟩ ((psynced → asynced) ∧ err = err0)

User applied rule call right

And obtained the following new goals

Proof step 7:
isdir0 ↔ isdir, 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, mode = MODE_R, inode = ? in {err := ESUCCESS; vfs_walk#(path, user, dirs, files, asynced; ino, err); if err = ESUCCESS then let isdir = false in vfs_may_open#(ino, isdir, mode, 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)}] ⟨posix_fsync#(path, isdir, user, root, abs-files(files), abs-of(of); ; psynced, err0)⟩ ((psynced → asynced) ∧ err = err0)

Rule argument

pos: right 1

Additional information

Used simplifier rules: vfs_fsync#(PATH, ISDATASYNC, USER, DIRS, FILES; ASYNCED; ERR) {let INO = ROOT_INO, MODE = MODE_R, INODE = ? in {ERR := ESUCCESS; vfs_walk#(PATH, USER, DIRS, FILES, ASYNCED; INO, ERR); if ERR = ESUCCESS then let ISDIR = false in vfs_may_open# (INO, ISDIR, MODE, USER, DIRS, FILES, ASYNCED; INODE, ERR); if ERR = ESUCCESS then afs_fsync#(INODE, ISDATASYNC, DIRS, FILES; ; ASYNCED, ERR); if ERR = ESUCCESS then afs_sync#(DIRS, FILES; ; ASYNCED, ERR)} };