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Proof step 45 from proof refine-mkdir (previous step)

root[q].dir? ↔ ino1 ∈ dirs, dent = negdentry((q + str ').last), err = ESUCCESS, err1 = ENOTDIR, err2 = err3, err3 = ESUCCESS, fs = abs-files(files), 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(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pre-iget(ino, dirs, files), px-parent(user, q, ROOT_INO, dirs, files), psynced → asynced ⊦ ⟨posix_mkdir#(q + str ', md, user, fs, abs-of(of); err0, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err1 = err0), q + str ' = ε, inode.directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 46:
root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), px-parent(user, q, ROOT_INO, dirs, files), ROOT_INO ∈ dirs, ino1 ∈ files, ¬ root[q].dir?, ¬ ino1 ∈ dirs, psynced → asynced ⊦ ⟨posix_mkdir#(q + str ', md, user, abs-files(files), abs-of(of); err0, root; psynced)⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ENOTDIR = 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)% ⊦ 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)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]% ⊦ p + str ' ≠ ε; (s)