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Proof step 49 from proof refine-close (previous step)

files[ino].nlink = 0, files[m] = mkfile(m1, md, m2, content), of0[fd] = mkfile(m, mode, m0), err = ESUCCESS, fs = abs-files(files), ino = inode.ino, inode = mkinode(m, md, false, m2, 0, m1), ofh = abs-of(of0), root.dir?, dom of0 < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), afs-cons(dirs, files -- ino), fids-cons(root, abs-files(files), abs-of(of0)), of-cons(of0, dirs, files), of-cons(of0 -- fd, dirs, files -- ino), pre-evict(inode, dirs, files), fd ∈ of0, psynced → asynced ⊦ ⟨posix_close#(fd, user, root; err0, fs, ofh)⟩ (ofh = abs-of(of0 -- fd) ∧ fs = abs-files(files -- ino) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ESUCCESS = err0), is-open(m, of0 -- fd), ino ∈ dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 50:
# links(m, dirs) = 0, files[m] = mkfile(m1, md, 0, content), of0[fd] = mkfile(m, mode, m0), fs = abs-files(files), ofh = abs-of(of0), m ≠ ROOT_INO, root.dir?, dom of0 < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files -- m), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of0)), of-cons(of0, dirs, files), of-cons(of0 -- fd, dirs, files -- m), m ∈ files, fd ∈ of0, ¬ is-open(m, of0 -- fd), psynced → asynced ⊦ ⟨posix_close#(fd, user, root; err0, fs, ofh)⟩ (ofh = abs-of(of0 -- fd) ∧ fs = abs-files(files -- m) ∧ (psynced → asynced) ∧ ESUCCESS = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ of-cons(of, dirs, files) ∧ fd ∈ of ∧ of[fd] = mkfile(ino, mode, n) → ino ∈ files; (ss)%⊦ afs-cons(dirs, files) → ( links(ino, dirs) = ∅ ↔ (ino ∈ dirs → dirs[ino].nlink = 0) ∧ (ino ∈ files → files[ino].nlink = 0)); (ws)%size-zero-02: ⊦ # ls = 0 → ls = ∅; (forward) from specification set-basic[alink-set]% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)%afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)%⊦ of-cons(of, dirs, files) ∧ fd ∈ of ∧ of[fd] = mkfile(ino, mode, n) ∧ afs-cons(dirs, files) → ¬ ino ∈ dirs; (s)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)%⊦ valid-dir-inode(inode, dirs, files) ↔ valid-dir-ino(inode.ino, dirs, files) ∧ inode.nlink = dirs[inode.ino].nlink ∧ inode.size = dirs[inode.ino].size ∧ inode.nsubdirs = dirs[inode.ino].nsubdirs ∧ inode.directory; (s)%⊦ valid-wb-inode(inode, dirs, files) ↔ valid-dir-inode(inode, dirs, files) ∨ valid-file-inode(inode, dirs, files); (s)%⊦ pre-evict(inode, dirs, files) ↔ valid-wb-inode(inode, dirs, files) ∧ inode.ino ≠ ROOT_INO; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)