Proof step 44 from proof inv-unlink (previous step)

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

• Proof step 45:

  # links(entries0[str], dirs0) = m1 + 1, (entries0[str] = ino ⊃ links(entries0[str], dirs0) -- mklink(m, str);links(ino, dirs0)) = ∅, (ino = entries0[str] ⊃ mkfile(m0, md1, m1, content);mkfile(m4, md, m5, content0)) = mkfile(m6, md0, m7, content1), (ino = m ⊃ mkdir(m2, md2, # links(m, dirs0), m3, entries0 -- str);mkdir(m8, md3, m9, m10, entries)) = mkdir(m11, md4, m12, m13, entries1), files0[ino] = mkfile(m4, md, m5, content0), files0[entries0[str]] = mkfile(m0, md1, m1 + 1, content), dirs0[m] = mkdir(m2 + 1, md2, # links(m, dirs0), m3, entries0), dirs0[ino] = mkdir(m8, md3, m9, m10, entries), afs-cons(dirs0, files0), ino ∈ dirs0, m ∈ dirs0, str ∈ entries0, entries0[str] ∈ files0, ROOT_INO ∈ dirs0, ino ∈ dirs0 → m9 = # links(ino, dirs0) ∧ # links(ino, dirs0) ≤ 1 ∧ m8 = # entries ∧ m10 = # subdirs(ino, dirs0), ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries = ∅, ino ∈ files0 → ¬ ino ∈ dirs0 ∧ m5 = # links(ino, dirs0), ino ∈ dirs0 ∧ name ∈ entries → entries[name] ∈ dirs0 ∨ entries[name] ∈ files0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries1 = ∅, ino = ROOT_INO

• Proof step 47:

  # links(entries0[str], dirs0) = m1 + 1, (ino = entries0[str] ⊃ mkfile(m0, md1, m1, content);mkfile(m4, md, m5, content0)) = mkfile(m6, md0, m7, content1), (ino = m ⊃ mkdir(m2, md2, # links(m, dirs0), m3, entries0 -- str);mkdir(m8, md3, m9, m10, entries)) = mkdir(m11, md4, m12, m13, entries1), files0[ino] = mkfile(m4, md, m5, content0), files0[entries0[str]] = mkfile(m0, md1, m1 + 1, content), dirs0[m] = mkdir(m2 + 1, md2, # links(m, dirs0), m3, entries0), dirs0[ino] = mkdir(m8, md3, m9, m10, entries), afs-cons(dirs0, files0), ino ∈ dirs0, m ∈ dirs0, str ∈ entries0, entries0[str] ∈ files0, ROOT_INO ∈ dirs0, ino ∈ dirs0 → m9 = # links(ino, dirs0) ∧ # links(ino, dirs0) ≤ 1 ∧ m8 = # entries ∧ m10 = # subdirs(ino, dirs0), ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries = ∅, ino ∈ files0 → ¬ ino ∈ dirs0 ∧ m5 = # links(ino, dirs0), ino ∈ dirs0 ∧ name ∈ entries → entries[name] ∈ dirs0 ∨ entries[name] ∈ files0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ m12 = # (entries0[str] = ino ⊃ links(entries0[str], dirs0) -- mklink(m, str);links(ino, dirs0)) ∧ # (entries0[str] = ino ⊃ links(entries0[str], dirs0) -- mklink(m, str);links(ino, dirs0)) ≤ 1 ∧ m11 = # entries1 ∧ m13 = # subdirs(ino, dirs0[m, mkdir(m2, md2, # links(m, dirs0), m3, entries0 -- str)])

• Proof step 51:

  # links(entries0[str], dirs0) = m1 + 1, (ino = entries0[str] ⊃ mkfile(m0, md1, m1, content);mkfile(m4, md, m5, content0)) = mkfile(m6, md0, m7, content1), (ino = m ⊃ mkdir(m2, md2, # links(m, dirs0), m3, entries0 -- str);mkdir(m8, md3, m9, m10, entries)) = mkdir(m11, md4, m12, m13, entries1), files0[ino] = mkfile(m4, md, m5, content0), files0[entries0[str]] = mkfile(m0, md1, m1 + 1, content), dirs0[m] = mkdir(m2 + 1, md2, # links(m, dirs0), m3, entries0), dirs0[ino] = mkdir(m8, md3, m9, m10, entries), afs-cons(dirs0, files0), ino ∈ files0, m ∈ dirs0, str ∈ entries0, entries0[str] ∈ files0, ROOT_INO ∈ dirs0, ino ∈ dirs0 → m9 = # links(ino, dirs0) ∧ # links(ino, dirs0) ≤ 1 ∧ m8 = # entries ∧ m10 = # subdirs(ino, dirs0), ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries = ∅, ino ∈ files0 → ¬ ino ∈ dirs0 ∧ m5 = # links(ino, dirs0), ino ∈ dirs0 ∧ name ∈ entries → entries[name] ∈ dirs0 ∨ entries[name] ∈ files0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ¬ ino ∈ dirs0 ∧ m7 = # (entries0[str] = ino ⊃ links(entries0[str], dirs0) -- mklink(m, str);links(ino, dirs0))

• Proof step 55:

  # links(entries0[str], dirs0) = m1 + 1, (ino = entries0[str] ⊃ mkfile(m0, md1, m1, content);mkfile(m4, md, m5, content0)) = mkfile(m6, md0, m7, content1), (ino = m ⊃ mkdir(m2, md2, # links(m, dirs0), m3, entries0 -- str);mkdir(m8, md3, m9, m10, entries)) = mkdir(m11, md4, m12, m13, entries1), files0[ino] = mkfile(m4, md, m5, content0), files0[entries0[str]] = mkfile(m0, md1, m1 + 1, content), dirs0[m] = mkdir(m2 + 1, md2, # links(m, dirs0), m3, entries0), dirs0[ino] = mkdir(m8, md3, m9, m10, entries), afs-cons(dirs0, files0), ino ∈ dirs0, name ∈ entries1, m ∈ dirs0, str ∈ entries0, entries0[str] ∈ files0, ROOT_INO ∈ dirs0, ino ∈ dirs0 → m9 = # links(ino, dirs0) ∧ # links(ino, dirs0) ≤ 1 ∧ m8 = # entries ∧ m10 = # subdirs(ino, dirs0), ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries = ∅, ino ∈ files0 → ¬ ino ∈ dirs0 ∧ m5 = # links(ino, dirs0), ino ∈ dirs0 ∧ name ∈ entries → entries[name] ∈ dirs0 ∨ entries[name] ∈ files0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries1[name] ∈ dirs0, entries1[name] ∈ files0

• Proof step 59:

  # links(entries0[str], dirs0) = m1 + 1, (ino = entries0[str] ⊃ mkfile(m0, md1, m1, content);mkfile(m4, md, m5, content0)) = mkfile(m6, md0, m7, content1), (ino = m ⊃ mkdir(m2, md2, # links(m, dirs0), m3, entries0 -- str);mkdir(m8, md3, m9, m10, entries)) = mkdir(m11, md4, m12, m13, entries1), files0[ino] = mkfile(m4, md, m5, content0), files0[entries0[str]] = mkfile(m0, md1, m1 + 1, content), dirs0[m] = mkdir(m2 + 1, md2, # links(m, dirs0), m3, entries0), dirs0[ino] = mkdir(m8, md3, m9, m10, entries), afs-cons(dirs0, files0), ino ∈ files0, n ∈ content1, m ∈ dirs0, str ∈ entries0, entries0[str] ∈ files0, ROOT_INO ∈ dirs0, ino ∈ dirs0 → m9 = # links(ino, dirs0) ∧ # links(ino, dirs0) ≤ 1 ∧ m8 = # entries ∧ m10 = # subdirs(ino, dirs0), ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries = ∅, ino ∈ files0 → ¬ ino ∈ dirs0 ∧ m5 = # links(ino, dirs0), ino ∈ dirs0 ∧ name ∈ entries → entries[name] ∈ dirs0 ∨ entries[name] ∈ files0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ # content1[n] = VFS_PAGE_SIZE

Rule argument

Additional information