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Proof step 64 from proof inv-rmdir (previous step)

# links(entries0[str], dirs0) = m2 + 1, (ino = entries0[str] ⊃ mkdir(m5, md1, m2, m7, ∅) ;(ino = m ⊃ mkdir(m3, md3, # links(m, dirs0), m0, entries0 -- str) ;mkdir(# entries1, md0, # links(ino, dirs0), # subdirs(ino, dirs0), entries1) ) ) = mkdir(m12, md4, m13, m14, entries2), dirs0[m] = mkdir(m3 + 1, md3, # links(m, dirs0), m0 + 1, entries0), dirs0[entries0[str]] = mkdir(m5, md1, m2 + 1, m7, ∅), files[ino] = mkfile(m6, md, m8, content), dirs0[ino] = mkdir(# entries1, md0, # links(ino, dirs0), # subdirs(ino, dirs0), entries1), afs-cons(dirs0, files), ino ∈ dirs0, entries0[str] ∈ dirs0, ROOT_INO ∈ dirs0, m ∈ dirs0, str ∈ entries0, # links(ino, dirs0) ≤ 1, name ∈ entries1 → entries1[name] ∈ dirs0 ∨ entries1[name] ∈ files, ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries1 = ∅, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries0[str] = ROOT_INO, entries0[str] = m, # (entries0[str] = ino ⊃ links(entries0[str], dirs0) -- mklink(m, str);links(ino, dirs0)) ≤ 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 65:
# links(entries0[str], dirs0) = m2 + 1, (ino = entries0[str] ⊃ mkdir(m5, md1, m2, m7, ∅) ;(ino = m ⊃ mkdir(m3, md3, # links(m, dirs0), m0, entries0 -- str) ;mkdir(# entries1, md0, # links(ino, dirs0), # subdirs(ino, dirs0), entries1) ) ) = mkdir(m12, md4, m13, m14, entries2), dirs0[m] = mkdir(m3 + 1, md3, # links(m, dirs0), m0 + 1, entries0), dirs0[entries0[str]] = mkdir(m5, md1, m2 + 1, m7, ∅), files[ino] = mkfile(m6, md, m8, content), dirs0[ino] = mkdir(# entries1, md0, # links(ino, dirs0), # subdirs(ino, dirs0), entries1), afs-cons(dirs0, files), ino ∈ dirs0, entries0[str] ∈ dirs0, ROOT_INO ∈ dirs0, m ∈ dirs0, str ∈ entries0, # links(ino, dirs0) ≤ 1, name ∈ entries1 → entries1[name] ∈ dirs0 ∨ entries1[name] ∈ files, ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries1 = ∅, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ # (entries0[str] = ino ⊃ links(entries0[str], dirs0) -- mklink(m, str);links(ino, dirs0)) = 1, # (entries0[str] = ino ⊃ links(entries0[str], dirs0) -- mklink(m, str);links(ino, dirs0)) = 0, (entries0[str] = ino ⊃ links(entries0[str], dirs0) -- mklink(m, str);links(ino, dirs0)) = ∅, entries0[str] = ROOT_INO, entries0[str] = m

Rule argument

Additional information

Used simplifier rules: size-zero-01: ⊦ ls ≠ ∅ → # ls ≠ 0; (forward) from specification set-basic[alink-set]%size-zero: ⊦ # ls ≠ 0 → ls ≠ ∅; (forward) from specification set-basic[alink-set]% ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)