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

(ino0 = m ⊃ mkdir(m0 + 1, md0, # links(m, dirs), m2, entries[str, ino]);mkdir(m6, md3, m7, m8, entries0)) = mkdir(m9, md4, m10, m11, entries1), dirs[ino0] = mkdir(m6, md3, m7, m8, entries0), dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), files[ino0] = mkfile(m1, md1, m3, content), (files ++ ino)[ino0] = mkfile(m4, md2, m5, content0), afs-cons(dirs, files), m ∈ dirs, ROOT_INO ∈ dirs, ino0 ∈ dirs ∧ ino0 ≠ ROOT_INO ∧ links(ino0, dirs) = ∅ → entries0 = ∅, ino0 ∈ dirs ∧ name ∈ entries0 → entries0[name] ∈ dirs ∨ entries0[name] ∈ files, ino0 ∈ dirs → m7 = # links(ino0, dirs) ∧ # links(ino0, dirs) ≤ 1 ∧ m6 = # entries0 ∧ m8 = # subdirs(ino0, dirs), links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ino = 0, ino0 = ino, ino0 ∈ files, str ∈ entries, ino ∈ dirs, ino ∈ files, (ino0 ∈ dirs ∧ ino0 ≠ ROOT_INO ∧ links(ino0, dirs) = ∅ → entries1 = ∅) ∧ ( ino0 ∈ dirs → m10 = # links(ino0, dirs) ∧ # links(ino0, dirs) ≤ 1 ∧ m9 = # entries1 ∧ m11 = # subdirs(ino0, dirs[m, mkdir(m0, md0, # links(m, dirs), m2, entries[str, ino])])) ∧ (ino0 ∈ dirs ∧ name ∈ entries1 → entries1[name] ∈ dirs ∨ entries1[name] = ino ∨ entries1[name] ∈ files)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 29:
(ino0 = m ⊃ mkdir(m0 + 1, md0, # links(m, dirs), m2, entries[str, ino]);mkdir(m6, md3, m7, m8, entries0)) = mkdir(m9, md4, m10, m11, entries1), (files ++ ino)[ino0] = mkfile(m4, md2, m5, content0), files[ino0] = mkfile(m1, md1, m3, content), dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), dirs[ino0] = mkdir(m6, md3, m7, m8, entries0), ino0 = m, afs-cons(dirs, files), ROOT_INO ∈ dirs, m ∈ dirs, ino0 ∈ dirs → m7 = # links(ino0, dirs) ∧ # links(ino0, dirs) ≤ 1 ∧ m6 = # entries0 ∧ m8 = # subdirs(ino0, dirs), ino0 ∈ dirs ∧ name ∈ entries0 → entries0[name] ∈ dirs ∨ entries0[name] ∈ files, ino0 ∈ dirs ∧ ino0 ≠ ROOT_INO ∧ links(ino0, dirs) = ∅ → entries0 = ∅, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ino = 0, ino0 = ino, ino ∈ files, ino ∈ dirs, str ∈ entries, ino0 ∈ files, (ino0 ∈ dirs ∧ ino0 ≠ ROOT_INO ∧ links(ino0, dirs) = ∅ → entries1 = ∅) ∧ ( ino0 ∈ dirs → m10 = # links(ino0, dirs) ∧ # links(ino0, dirs) ≤ 1 ∧ m9 = # entries1 ∧ m11 = # subdirs(ino0, dirs[m, mkdir(m0, md0, # links(m, dirs), m2, entries[str, ino])])) ∧ (ino0 ∈ dirs ∧ name ∈ entries1 → entries1[name] ∈ dirs ∨ entries1[name] = ino ∨ entries1[name] ∈ files)

Rule argument

fma: ino0 = m

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)% ⊦ ino0 ≠ ino1 → subdirs(ino0, dirs[ino1, ad]) = subdirs(ino0, dirs); (s)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)%⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) ∧ str ∈ entries ∧ afs-cons(dirs, files) → (entries[str] ∈ files ↔ ¬ entries[str] ∈ dirs); (ss) Used formulas: ino0 = m