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Proof step 17 from proof inv-mkdir (previous step)

# links(m, dirs) = m1, dirs[m] = mkdir(m0, md2, # links(m, dirs), m2, entries0), dent = negdentry(str), ino ≠ 0, afs-cons(dirs, files), m ∈ dirs, ¬ ino ∈ dirs, ¬ ino ∈ files, ¬ str ∈ entries0, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_mkdir_ino#(m, md, ino; dent, err, dirs)] ( afs-cons(dirs, files) → ⟪afs_inode_sync#(mkinode(m, md0, true, m1, m2, m0); dirs, files); p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := getinode(dent.ino, dirs, files); asynced := ?⟫ afs-cons(dirs, files))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 18:
# links(m, dirs) = m1, dirs[m] = mkdir(m0, md2, # links(m, dirs), m2, entries0), dent = negdentry(str), p_ino = m, afs-cons(dirs, files), m ∈ dirs, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [dirs[p_ino].entries[dent.name] := ino; dirs[p_ino].size := dirs[p_ino].size + 1; dirs[p_ino].nsubdirs := dirs[p_ino].nsubdirs + 1; dirs := dirs ++ ino; dirs[ino] := mkdir(0, md, 1, 0, ∅); dent := mkdentry(dent.name, ino); err := ESUCCESS] ( afs-cons(dirs, files) → ⟪afs_inode_sync#(mkinode(m, md0, true, m1, m2, m0); dirs, files); p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := getinode(dent.ino, dirs, files); asynced := ?⟫ afs-cons(dirs, files)), ino = 0, ino ∈ dirs, ino ∈ files, str ∈ entries0

Rule argument

pos: right 1

Additional information

Used simplifier rules: mkdir-ino: ⊦ ;