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Proof step 9 from proof inv-create (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), m ∈ dirs, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪if pre-create(p_inode, dent, md, dirs, files) then { {choose ino with ¬ ino ∈ dirs ∧ ¬ ino ∈ files ∧ ino ≠ 0 in 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)} or fail#(; ; err); asynced := ?} else abort⟫ afs-cons(dirs, files), str ∈ entries

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 10:
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-create(p_inode, dent, md, dirs, files), m ∈ dirs, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪if pre-create(p_inode, dent, md, dirs, files) then { {choose ino with ¬ ino ∈ dirs ∧ ¬ ino ∈ files ∧ ino ≠ 0 in 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)} or fail#(; ; err); asynced := ?} else abort⟫ afs-cons(dirs, files), str ∈ entries

Rule argument

fma: pre-create(p_inode, dent, md, dirs, files)

Additional information

Used simplifier rules: ⊦ pre-create(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)% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)% ⊦ mkdir(m, md, m0, m1, entries).size = m; (s)% ⊦ mkdir(m, md, m0, m1, entries).nsubdirs = m1; (s) Used formulas: pre-create(p_inode, dent, md, dirs, files)