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Proof step 140 from proof refine-create (previous step)

dirs[ino1] = mkdir(# entries, md0, # links(ino1, dirs), m1, entries), dent = negdentry(str), err = ESUCCESS, fs = abs-files(files), inode = mkinode(ino1, md0, true, # links(ino1, dirs), m1, # entries), p_inode = inode, root.dir?, root[q].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-create(p_inode, dent, md, dirs, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), ino1 ∈ dirs, psynced → asynced0, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [afs_create_ino#(p_inode.ino, md, ino; dent, err, dirs, files); afs_inode_sync#(p_inode; dirs, files); p_inode := getinode(p_inode.ino, dirs, files); c_inode := getinode(dent.ino, dirs, files); asynced := ?] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_create#(q + str ', md, user, abs-of(of); err2, root, fs; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err2)), ino = 0, str ∈ entries, ino ∈ files, ino ∈ dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 141:
# entries = dirs[ino1].size, # links(ino1, dirs) = dirs[ino1].nlink, dirs[ino1] = mkdir(# entries, md0, dirs[ino1].nlink, dirs[ino1].nsubdirs, entries), dent = negdentry(str), err = ESUCCESS, fs = abs-files(files), inode = mkinode(ino1, md0, true, dirs[ino1].nlink, dirs[ino1].nsubdirs, # entries), ino ≠ 0, root.dir?, root[q].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), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), ino1 ∈ dirs, ¬ str ∈ dirs[ino1].entries, ¬ str ∈ entries, ¬ ino ∈ files, ¬ ino ∈ dirs, psynced → asynced0, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [afs_create_ino#(ino1, md, ino; dent, err, dirs, files); afs_inode_sync#(inode; dirs, files); inode := (inode.ino ∈ dirs ⊃ mkinode(inode.ino, dirs[inode.ino].meta, true, dirs[inode.ino].nlink, dirs[inode.ino].nsubdirs, dirs[inode.ino].size) ;mkinode(inode.ino, files[inode.ino].meta, false, files[inode.ino].nlink, 0, files[inode.ino].size) ); c_inode := getinode(dent.ino, dirs, files); asynced := ?] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_create#(q + str ', md, user, abs-of(of); err2, root, fs; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err2))

Rule argument

Additional information

Used simplifier rules: afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base%⊦ 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)% ⊦ 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).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (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)% ⊦ negdentry(str).negdentry?; (s)% ⊦ negdentry(str).name = str; (s)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)%⊦ valid-negdentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ ¬ dent.name ∈ dirs[ino].entries ∧ dent.negdentry?; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%⊦ pre-create(p_inode, dent, md, dirs, files) ↔ valid-negdentry(p_inode.ino, dent, dirs, files) ∧ valid-dir-inode(p_inode, dirs, files); (s)