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Proof step 272 from proof afs-cons-rename-file-dentry (previous step)

(ino = m ⊃ mkdir(m1, md2, # links(m, dirs0), m4, entries1);mkdir(m8, md5, m9, m10, entries)) = mkdir(m11, md6, m12, m13, entries0), (ino = entries1[str0] ⊃ mkfile(m2, md, # links(entries1[str0], dirs0), content1);mkfile(m3, md3, m5, content)) = mkfile(m6, md4, m7, content0), dirs0[ino] = mkdir(m8, md5, m9, m10, entries), files[entries1[str0]] = mkfile(m0, md0, # links(entries1[str0], dirs0), content1), dirs0[m] = mkdir(m1, md1, # links(m, dirs0), m4, entries1), files[ino] = mkfile(m3, md3, m5, content), afs-cons(dirs0, files), m ∈ dirs0, entries1[str0] ∈ files, str0 ∈ entries1, ROOT_INO ∈ dirs0, ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries = ∅, ino ∈ files → ¬ ino ∈ dirs0 ∧ m5 = # links(ino, dirs0), ino ∈ dirs0 ∧ name ∈ entries → entries[name] ∈ dirs0 ∨ entries[name] ∈ files, ino ∈ dirs0 → m9 = # links(ino, dirs0) ∧ # links(ino, dirs0) ≤ 1 ∧ m8 = # entries ∧ m10 = # subdirs(ino, dirs0), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries1[str0] ∈ dirs0, (ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries0 = ∅) ∧ (ino ∈ dirs0 → m12 = # links(ino, dirs0) ∧ # links(ino, dirs0) ≤ 1 ∧ m11 = # entries0 ∧ m13 = # subdirs(ino, dirs0)) ∧ (ino ∈ files → ¬ ino ∈ dirs0 ∧ m7 = # links(ino, dirs0)) ∧ (ino ∈ dirs0 ∧ name ∈ entries0 → entries0[name] ∈ dirs0 ∨ entries0[name] ∈ files) ∧ (ino ∈ files ∧ n ∈ content0 → # content0[n] = VFS_PAGE_SIZE)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 273:
(ino = entries1[str0] ⊃ mkfile(m2, md, # links(entries1[str0], dirs0), content1);mkfile(m3, md3, m5, content)) = mkfile(m6, md4, m7, content0), (ino = m ⊃ mkdir(m1, md2, # links(m, dirs0), m4, entries1);mkdir(m8, md5, m9, m10, entries)) = mkdir(m11, md6, m12, m13, entries0), files[ino] = mkfile(m3, md3, m5, content), dirs0[m] = mkdir(m1, md1, # links(m, dirs0), m4, entries1), files[entries1[str0]] = mkfile(m0, md0, # links(entries1[str0], dirs0), content1), dirs0[ino] = mkdir(m8, md5, m9, m10, entries), afs-cons(dirs0, files), ROOT_INO ∈ dirs0, str0 ∈ entries1, entries1[str0] ∈ files, m ∈ dirs0, ino ∈ dirs0 → m9 = # links(ino, dirs0) ∧ # links(ino, dirs0) ≤ 1 ∧ m8 = # entries ∧ m10 = # subdirs(ino, dirs0), ino ∈ dirs0 ∧ name ∈ entries → entries[name] ∈ dirs0 ∨ entries[name] ∈ files, ino ∈ files → ¬ ino ∈ dirs0 ∧ m5 = # links(ino, dirs0), ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries = ∅, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ino = m, entries1[str0] ∈ dirs0, (ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries0 = ∅) ∧ (ino ∈ dirs0 → m12 = # links(ino, dirs0) ∧ # links(ino, dirs0) ≤ 1 ∧ m11 = # entries0 ∧ m13 = # subdirs(ino, dirs0)) ∧ (ino ∈ files → ¬ ino ∈ dirs0 ∧ m7 = # links(ino, dirs0)) ∧ (ino ∈ dirs0 ∧ name ∈ entries0 → entries0[name] ∈ dirs0 ∨ entries0[name] ∈ files) ∧ (ino ∈ files ∧ n ∈ content0 → # content0[n] = VFS_PAGE_SIZE)

Rule argument

fma: ino = 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)%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (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 = m