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Proof step 28 from proof afs-cons-mkdir-ino (previous step)

dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), files[ino0] = mkfile(m1, md1, m3, content), dirs[ino0] = mkdir(m4, md2, m5, m6, entries0), ino0 = ino, mkdir(0, md, 1, 0, ∅) = mkdir(m7, md3, m8, m9, entries1), afs-cons(dirs, files), m ∈ dirs, ROOT_INO ∈ dirs, ino0 ∈ dirs → m5 = # links(ino0, dirs) ∧ # links(ino0, dirs) ≤ 1 ∧ m4 = # entries0 ∧ m6 = # subdirs(ino0, dirs), ino0 ∈ dirs ∧ ino0 ≠ ROOT_INO ∧ links(ino0, dirs) = ∅ → entries0 = ∅, ino0 ∈ files → ¬ ino0 ∈ dirs ∧ m3 = # links(ino0, dirs), ino0 ∈ dirs ∧ name ∈ entries0 → entries0[name] ∈ dirs ∨ entries0[name] ∈ files, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ino = 0, ino ∈ dirs, ino ∈ files, str ∈ entries, ((ino0 = ino ∨ ino0 ∈ dirs) ∧ ino0 ≠ ROOT_INO ∧ (ino = ino0 ⊃ ∅ ++ mklink(m, str);links(ino0, dirs)) = ∅ → entries1 = ∅) ∧ ( ino0 = ino ∨ ino0 ∈ dirs → ¬ ino0 ∈ files ∧ m8 = # (ino = ino0 ⊃ ∅ ++ mklink(m, str);links(ino0, dirs)) ∧ # (ino = ino0 ⊃ ∅ ++ mklink(m, str);links(ino0, dirs)) ≤ 1 ∧ m7 = # entries1 ∧ m9 = # subdirs(ino0, (dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino, mkdir(0, md, 1, 0, ∅)])) ∧ ((ino0 = ino ∨ ino0 ∈ dirs) ∧ name ∈ entries1 → entries1[name] = ino ∨ entries1[name] ∈ dirs ∨ entries1[name] ∈ files)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
dirs[ino] = mkdir(m4, md2, m5, m6, entries0), files[ino] = mkfile(m1, md1, m3, content), dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), afs-cons(dirs, files), ROOT_INO ∈ dirs, m ∈ dirs, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ 0 = # subdirs(ino, (dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino, mkdir(0, md, 1, 0, ∅)]), ino = 0, subdirs(ino, (dirs[m, mkdir(m0 + 1, md0, # links(m, dirs), m2 + 1, entries[str, ino])] ++ ino)[ino, mkdir(0, md, 1, 0, ∅)]) = ∅, str ∈ entries, ino ∈ files, ino ∈ dirs

Rule argument

Additional information

Used simplifier rules: size-zero-01: ⊦ strings ≠ ∅ → # strings ≠ 0; (forward) from specification set-basic[dir-entries]%size-zero: ⊦ # strings ≠ 0 → strings ≠ ∅; (forward) from specification set-basic[dir-entries]% ⊦ ¬ str ∈ ∅; (s)% ⊦ # ∅ = 0; (s)% ⊦ #(∅ ++ alink) = 1; (s)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)