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Proof step 382 from proof afs-cons-rename-dir-dentry (previous step)

(ino = entries0[str0] ⊃ mkdir(m3, md, # links(entries0[str0], dirs0), m6, ∅) ;(ino = m ⊃ mkdir(m1, md2, # links(m, dirs0), m4, entries0);mkdir(m5, md4, m7, m8, entries)) ) = mkdir(m9, md5, m10, m11, entries1), dirs0[ino] = mkdir(m5, md4, m7, m8, entries), files[ino] = mkfile(m0, md0, m2, content), dirs0[entries0[str0]] = mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅), dirs0[m] = mkdir(m1, md1, # links(m, dirs0), m4, entries0), afs-cons(dirs0, files), m ∈ dirs0, str0 ∈ entries0, entries0[str0] ∈ dirs0, ROOT_INO ∈ dirs0, ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries = ∅, ino ∈ files → ¬ ino ∈ dirs0 ∧ m2 = # links(ino, dirs0), ino ∈ dirs0 ∧ name ∈ entries → entries[name] ∈ dirs0 ∨ entries[name] ∈ files, ino ∈ dirs0 → m7 = # links(ino, dirs0) ∧ # links(ino, dirs0) ≤ 1 ∧ m5 = # entries ∧ m8 = # subdirs(ino, dirs0), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries0[str0] = m, entries0[str0] = ROOT_INO, (ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries1 = ∅) ∧ ( ino ∈ dirs0 → m10 = # links(ino, dirs0) ∧ # links(ino, dirs0) ≤ 1 ∧ m9 = # entries1 ∧ m11 = # subdirs (ino, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)][entries0[str0], mkdir(m3, md, # links(entries0[str0], dirs0), m6, ∅)])) ∧ (ino ∈ dirs0 ∧ name ∈ entries1 → entries1[name] ∈ dirs0 ∨ entries1[name] ∈ files)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 383:
(ino = entries0[str0] ⊃ mkdir(m3, md, # links(entries0[str0], dirs0), m6, ∅) ;(ino = m ⊃ mkdir(m1, md2, # links(m, dirs0), m4, entries0);mkdir(m5, md4, m7, m8, entries)) ) = mkdir(m9, md5, m10, m11, entries1), dirs0[m] = mkdir(m1, md1, # links(m, dirs0), m4, entries0), dirs0[entries0[str0]] = mkdir(m3, md3, # links(entries0[str0], dirs0), m6, ∅), files[ino] = mkfile(m0, md0, m2, content), dirs0[ino] = mkdir(m5, md4, m7, m8, entries), afs-cons(dirs0, files), ROOT_INO ∈ dirs0, entries0[str0] ∈ dirs0, str0 ∈ entries0, m ∈ dirs0, ino ∈ dirs0 → m7 = # links(ino, dirs0) ∧ # links(ino, dirs0) ≤ 1 ∧ m5 = # entries ∧ m8 = # subdirs(ino, dirs0), ino ∈ dirs0 ∧ name ∈ entries → entries[name] ∈ dirs0 ∨ entries[name] ∈ files, ino ∈ files → ¬ ino ∈ dirs0 ∧ m2 = # links(ino, dirs0), ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries = ∅, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries0[str0] = ROOT_INO, entries0[str0] = m, ino = entries0[str0], (ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries1 = ∅) ∧ ( ino ∈ dirs0 → m10 = # links(ino, dirs0) ∧ # links(ino, dirs0) ≤ 1 ∧ m9 = # entries1 ∧ m11 = # subdirs (ino, dirs0[m, mkdir(m1, md2, # links(m, dirs0), m4, entries0)][entries0[str0], mkdir(m3, md, # links(entries0[str0], dirs0), m6, ∅)])) ∧ (ino ∈ dirs0 ∧ name ∈ entries1 → entries1[name] ∈ dirs0 ∨ entries1[name] ∈ files)

Rule argument

fma: ino = entries0[str0]

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)%⊦ p_ino ∈ dirs ∧ dirs[p_ino] = mkdir(m, md, n, n0, entries) ∧ str ∈ entries → links(entries[str], dirs) ≠ ∅; (s)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)%⊦ subdirs(ino, dirs[ino0, ad0][ino, ad]) = subdirs(ino, dirs[ino, ad]); (s)%⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(m0, md0, n1, n2, entries) → subdirs(ino0, dirs[ino, mkdir(m, md, n, n0, entries)]) = subdirs(ino0, dirs); (s)%afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base% ⊦ # ∅ = 0; (s)% ⊦ ¬ str ∈ ∅; (s) Used formulas: ino = entries0[str0]