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Proof step 48 from proof inv-link (previous step)

(ino = m ⊃ mkdir(m0 + 1, md1, # links(m, dirs0), m5, entries1[str0, entries[str]]);mkdir(m11, md5, m12, m13, entries2)) = mkdir(m14, md6, m15, m16, entries3), (ino = entries[str] ⊃ mkfile(m1, md4, # links(entries[str], dirs0) + 1, content0);mkfile(m3, md, m7, content)) = mkfile(m9, md0, m10, content1), dirs0[ino] = mkdir(m11, md5, m12, m13, entries2), dirs0[ino0] = mkdir(m2, md3, # links(ino0, dirs0), m6, entries0), files0[entries[str]] = mkfile(m1, md4, # links(entries[str], dirs0), content0), dirs0[m] = mkdir(m0, md1, # links(m, dirs0), m5, entries1), entries0[str] = entries[str], dirs0[ino1] = mkdir(m4, md2, # links(ino1, dirs0), m8, entries), files0[ino] = mkfile(m3, md, m7, content), afs-cons(dirs0, files0), ROOT_INO ∈ dirs0, entries[str] ∈ files0, m ∈ dirs0, str ∈ entries0, ino0 ∈ dirs0, ino1 ∈ dirs0, str ∈ entries, ino ∈ dirs0 ∧ name ∈ entries2 → entries2[name] ∈ dirs0 ∨ entries2[name] ∈ files0, ino ∈ files0 → ¬ ino ∈ dirs0 ∧ m7 = # links(ino, dirs0), ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries2 = ∅, ino ∈ dirs0 → m12 = # links(ino, dirs0) ∧ # links(ino, dirs0) ≤ 1 ∧ m11 = # entries2 ∧ m13 = # subdirs(ino, dirs0), links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(ino0, dirs0) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ str0 ∈ entries1, (ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ (entries[str] = ino ⊃ links(entries[str], dirs0) ++ mklink(m, str0);links(ino, dirs0)) = ∅ → entries3 = ∅) ∧ ( ino ∈ dirs0 → m15 = # (entries[str] = ino ⊃ links(entries[str], dirs0) ++ mklink(m, str0);links(ino, dirs0)) ∧ # (entries[str] = ino ⊃ links(entries[str], dirs0) ++ mklink(m, str0);links(ino, dirs0)) ≤ 1 ∧ m14 = # entries3 ∧ m16 = # subdirs(ino, dirs0[m, mkdir(m0, md1, # links(m, dirs0), m5, entries1[str0, entries[str]])])) ∧ (ino ∈ files0 → ¬ ino ∈ dirs0 ∧ m10 = # (entries[str] = ino ⊃ links(entries[str], dirs0) ++ mklink(m, str0);links(ino, dirs0))) ∧ (ino ∈ dirs0 ∧ name ∈ entries3 → entries3[name] ∈ dirs0 ∨ entries3[name] ∈ files0) ∧ (ino ∈ files0 ∧ n ∈ content1 → # content1[n] = VFS_PAGE_SIZE)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 49:
(ino = entries[str] ⊃ mkfile(m1, md4, # links(entries[str], dirs0) + 1, content0);mkfile(m3, md, m7, content)) = mkfile(m9, md0, m10, content1), (ino = m ⊃ mkdir(m0 + 1, md1, # links(m, dirs0), m5, entries1[str0, entries[str]]);mkdir(m11, md5, m12, m13, entries2)) = mkdir(m14, md6, m15, m16, entries3), files0[ino] = mkfile(m3, md, m7, content), dirs0[ino1] = mkdir(m4, md2, # links(ino1, dirs0), m8, entries), entries0[str] = entries[str], dirs0[m] = mkdir(m0, md1, # links(m, dirs0), m5, entries1), files0[entries[str]] = mkfile(m1, md4, # links(entries[str], dirs0), content0), dirs0[ino0] = mkdir(m2, md3, # links(ino0, dirs0), m6, entries0), dirs0[ino] = mkdir(m11, md5, m12, m13, entries2), afs-cons(dirs0, files0), str ∈ entries, ino1 ∈ dirs0, ino0 ∈ dirs0, str ∈ entries0, m ∈ dirs0, entries[str] ∈ files0, ROOT_INO ∈ dirs0, ino ∈ dirs0 → m12 = # links(ino, dirs0) ∧ # links(ino, dirs0) ≤ 1 ∧ m11 = # entries2 ∧ m13 = # subdirs(ino, dirs0), ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries2 = ∅, ino ∈ files0 → ¬ ino ∈ dirs0 ∧ m7 = # links(ino, dirs0), ino ∈ dirs0 ∧ name ∈ entries2 → entries2[name] ∈ dirs0 ∨ entries2[name] ∈ files0, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino0, dirs0) ≠ ∅ ∨ ino0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ino = entries[str], str0 ∈ entries1, (ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ (entries[str] = ino ⊃ links(entries[str], dirs0) ++ mklink(m, str0);links(ino, dirs0)) = ∅ → entries3 = ∅) ∧ ( ino ∈ dirs0 → m15 = # (entries[str] = ino ⊃ links(entries[str], dirs0) ++ mklink(m, str0);links(ino, dirs0)) ∧ # (entries[str] = ino ⊃ links(entries[str], dirs0) ++ mklink(m, str0);links(ino, dirs0)) ≤ 1 ∧ m14 = # entries3 ∧ m16 = # subdirs(ino, dirs0[m, mkdir(m0, md1, # links(m, dirs0), m5, entries1[str0, entries[str]])])) ∧ (ino ∈ files0 → ¬ ino ∈ dirs0 ∧ m10 = # (entries[str] = ino ⊃ links(entries[str], dirs0) ++ mklink(m, str0);links(ino, dirs0))) ∧ (ino ∈ dirs0 ∧ name ∈ entries3 → entries3[name] ∈ dirs0 ∨ entries3[name] ∈ files0) ∧ (ino ∈ files0 ∧ n ∈ content1 → # content1[n] = VFS_PAGE_SIZE)

Rule argument

fma: ino = entries[str]

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)%⊦ 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-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base% ⊦ # ls + 1 = #(ls ++ alink) ↔ ¬ alink ∈ ls; (s)%⊦ alink ∈ links(ino, dirs) ↔ alink.pino ∈ dirs ∧ alink.name ∈ dirs[alink.pino].entries ∧ ino = dirs[alink.pino].entries[alink.name]; (s)% ⊦ mklink(m, str).pino = m; (s)% ⊦ mklink(m, str).name = str; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ mkdir(m, md, m0, m1, entries).entries = entries; (s)%⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n0, content) ∧ n ∈ content → # content[n] = VFS_PAGE_SIZE; (s) Used formulas: ino = entries[str]