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Proof step 12 from proof inv-mkdir (previous step)

dirs[m] = mkdir(m0, md1, # links(m, dirs), m2, entries), dent = negdentry(str), p_inode = mkinode(m, md0, true, # links(m, dirs), m2, m0), afs-cons(dirs, files), pre-mkdir(p_inode, dent, md, dirs, files), m ∈ dirs, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪afs_mkdir_ino#(p_inode.ino, md, ino; dent, err, dirs); afs_inode_sync#(p_inode; dirs, files); p_inode := getinode(p_inode.ino, dirs, files); c_inode := getinode(dent.ino, dirs, files); asynced := ?⟫ afs-cons(dirs, files), ino = 0, str ∈ entries, ino ∈ files, ino ∈ dirs

User applied rule insert program lemma

And obtained the following new goals

Proof step 13:
afs-cons(dirs, files), pre-mkdir(p_inode, dent, md, dirs, files), ¬ ino ∈ dirs, ¬ ino ∈ files, ino ≠ 0 ⊦ ⟪afs_mkdir_ino#(p_inode.ino, md, ino; dent, err, dirs)⟫ afs-cons(dirs, files)
Proof step 14:
dirs[m] = mkdir(m0, md1, # links(m, dirs), m2, entries), dent = negdentry(str), files0 = files, ino0 = ino, md2 = md, p_inode = mkinode(m, md0, true, # links(m, dirs), m2, m0), p_inode0 = p_inode, afs-cons(dirs, files), pre-mkdir(p_inode, dent, md, dirs, files), m ∈ dirs, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_mkdir_ino#(p_inode.ino, md, ino; dent, err, dirs)] ( afs-cons(dirs, files0) → ⟪afs_inode_sync#(p_inode; dirs, files); p_inode := getinode(p_inode.ino, dirs, files); c_inode := getinode(dent.ino, dirs, files); asynced := ?⟫ afs-cons(dirs, files)), ino = 0, str ∈ entries, ino ∈ files, ino ∈ dirs

Rule argument

spec: <toplevel> name: afs-cons-mkdir-ino seq: afs-cons(dirs, files), pre-mkdir(p_inode, dent, md, dirs, files), ¬ ino ∈ dirs, ¬ ino ∈ files, ino ≠ 0 ⊦ ⟪afs_mkdir_ino#(p_inode.ino, md, ino; dent, err, dirs)⟫ afs-cons(dirs, files) subst: [ino, md, p_inode, dirs, err, dent, files] → [ino, md, p_inode, dirs, err, dent, files] flags: <all paths>

Additional information

Used simplifier rules: ⊦ pre-mkdir(p_inode, dent, md, dirs, files) ↔ valid-negdentry(p_inode.ino, dent, dirs, files) ∧ valid-dir-inode(p_inode, dirs, files); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%⊦ valid-negdentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ ¬ dent.name ∈ dirs[ino].entries ∧ dent.negdentry?; (s)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)% ⊦ negdentry(str).name = str; (s)% ⊦ negdentry(str).negdentry?; (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-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)