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Proof step 64 from proof refine-fsync (previous step)

root[path].dir? ↔ ino1 ∈ dirs, err = ESUCCESS, err1 = err, err2 = ESUCCESS, ino = ino1, inode = getinode(ino, dirs, files), 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, inode.meta), pre-iget(ino, dirs, files), px-parent(user, path, ROOT_INO, dirs, files), psynced → asynced ⊦ [afs_fsync#(inode, isdir0, dirs, files; ; asynced, err1); if err1 = ESUCCESS then afs_sync#(dirs, files; ; asynced, err1)] ⟨posix_fsync#(path, isdir0, user, root, abs-files(files), abs-of(of); ; psynced, err0)⟩ ((psynced → asynced) ∧ err1 = err0), inode.directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 65:
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, files[ino1].meta), px-parent(user, path, ROOT_INO, dirs, files), ROOT_INO ∈ dirs, ino1 ∈ files, ¬ root[path].dir?, ¬ ino1 ∈ dirs, psynced → asynced ⊦ [afs_fsync#(mkinode(ino1, files[ino1].meta, false, files[ino1].nlink, 0, files[ino1].size), 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)

Rule argument

Additional information

Used simplifier rules: path-in-dirs: p ≠ ε ⊦ ispath(p, n, m, dirs, files) → n ∈ dirs; (forward) from specification afs-base% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ px-parent(user, ε, ino, dirs, files); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ tree[ε] = tree; (s)%⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ pre-iget(ino, dirs, files) ↔ valid-ino(ino, dirs, files); (s)