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Proof step 67 from proof refine-fsync (previous step)

files[ino1] = mkfile(m, md, # links(ino1, dirs), content), root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pr(user, md), px-parent(user, path, ROOT_INO, dirs, files), ino1 ∈ files, ROOT_INO ∈ dirs, ¬ root[path].dir?, ¬ ino1 ∈ dirs, psynced → asynced ⊦ [afs_fsync#(mkinode(ino1, md, false, # links(ino1, dirs), 0, m), isdir0, dirs, files; ; asynced, err); if err = ESUCCESS then afs_sync#(dirs, files; ; asynced, err)] ⟨posix_fsync#(path, isdir0, 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 68:
isdir ↔ isdir0, files[ino1] = mkfile(m, md, # links(ino1, dirs), content), inode = mkinode(ino1, md, false, # links(ino1, dirs), 0, m), root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pr(user, md), px-parent(user, path, ROOT_INO, dirs, files), ROOT_INO ∈ dirs, ino1 ∈ files, psynced → asynced ⊦ [if valid-file-inode(inode, dirs, files) then {fail_or_success#(; ; err); choose bv with true in asynced := bv} else abort; if err = ESUCCESS then afs_sync#(dirs, files; ; asynced, err)] ⟨posix_fsync#(path, isdir0, user, root, abs-files(files), abs-of(of); ; psynced, err0)⟩ ((psynced → asynced) ∧ err = err0), root[path].dir?, ino1 ∈ dirs

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_fsync#(INODE, ISDATASYNC, DIRS, FILES; ; ASYNCED, ERR) {if valid-file-inode(INODE, DIRS, FILES) then {fail_or_success#(; ; ERR); choose bv with true in ASYNCED := bv} else abort };