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Proof step 26 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 ∈ files → ¬ ino0 ∈ dirs ∧ m3 = # links(ino0, dirs), 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, 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 ∈ files → ¬ ino0 ∈ dirs ∧ m5 = # links(ino0, dirs)) ∧ (ino0 ∈ dirs ∧ name ∈ entries1 → entries1[name] ∈ dirs ∨ entries1[name] = ino ∨ entries1[name] ∈ files) ∧ (ino0 ∈ files ∧ n ∈ content0 → # content0[n] = VFS_PAGE_SIZE)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 27:
(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), 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 ∈ files → ¬ ino0 ∈ dirs ∧ m3 = # links(ino0, dirs), 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 ∈ files → ¬ ino0 ∈ dirs ∧ m5 = # links(ino0, dirs)) ∧ (ino0 ∈ dirs ∧ name ∈ entries1 → entries1[name] ∈ dirs ∨ entries1[name] = ino ∨ entries1[name] ∈ files) ∧ (ino0 ∈ files ∧ n ∈ content0 → # content0[n] = VFS_PAGE_SIZE)

Rule argument

fma: ino0 ∈ files

Additional information

Used simplifier rules: ino ∈ files, ino0 ≠ 0, ¬ ino0 ∈ files ⊦ ino ≠ ino0 → (files ++ ino0)[ino] = files[ino]; (s)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)%⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (s)%afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws) Used formulas: ino0 ∈ files