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Proof step 79 from proof refine-fsync (previous step)

files[ino1] = mkfile(m0, md0, # links(ino1, dirs), content0), 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, md0), px-parent(user, path, ROOT_INO, dirs, files), ino1 ∈ files, ROOT_INO ∈ dirs, ¬ root[path].dir?, ¬ ino1 ∈ dirs, psynced → asynced0 ⊦ [afs_sync#(dirs, files; ; asynced, err0)] ⟨posix_fsync#(path, isdir0, user, root, abs-files(files), abs-of(of); ; psynced, err1)⟩ ((psynced → asynced) ∧ err0 = err1)

User applied rule call right

And obtained the following new goals

Proof step 80:
files[ino1] = mkfile(m0, md0, # links(ino1, dirs), content0), 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, md0), px-parent(user, path, ROOT_INO, dirs, files), ROOT_INO ∈ dirs, ino1 ∈ files, psynced → asynced0 ⊦ [fail_or_success#(; ; err); asynced := err = ESUCCESS] ⟨posix_fsync#(path, isdir0, user, root, abs-files(files), abs-of(of); ; psynced, err1)⟩ ((psynced → asynced) ∧ err = err1), root[path].dir?, ino1 ∈ dirs

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_sync#(DIRS, FILES; ; ASYNCED, ERR) {fail_or_success#(; ; ERR); ASYNCED := ERR = ESUCCESS};