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Proof step 66 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[ino] = mkdir(# entries1, md0, # links(ino, dirs0), # subdirs(ino, dirs0), entries1), files[ino] = mkfile(m6, md, m8, content), dirs0[entries0[str]] = mkdir(m5, md1, m2 + 1, m7, ∅), dirs0[m] = mkdir(m3 + 1, md3, # links(m, dirs0), m0 + 1, entries0), ino = entries0[str], afs-cons(dirs0, files), str ∈ entries0, m ∈ dirs0, ROOT_INO ∈ dirs0, entries0[str] ∈ dirs0, ino ∈ dirs0, # links(ino, dirs0) ≤ 1, ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries1 = ∅, name ∈ entries1 → entries1[name] ∈ dirs0 ∨ entries1[name] ∈ files, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ # (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)) = 1, (entries0[str] = ino ⊃ links(entries0[str], dirs0) -- mklink(m, str);links(ino, dirs0)) = ∅, entries0[str] = m, entries0[str] = ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 67:
# links(entries0[str], dirs0) = 1, dirs0[m] = mkdir(m3 + 1, md3, # links(m, dirs0), m0 + 1, entries0), files[entries0[str]] = mkfile(m6, md, m8, content), dirs0[entries0[str]] = mkdir(0, md1, 1, # subdirs(entries0[str], dirs0), ∅), afs-cons(dirs0, files), entries0[str] ∈ dirs0, ROOT_INO ∈ dirs0, m ∈ dirs0, str ∈ entries0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ #(links(entries0[str], dirs0) -- mklink(m, str)) = 1, #(links(entries0[str], dirs0) -- mklink(m, str)) = 0, entries0[str] = ROOT_INO, entries0[str] = m, links(entries0[str], dirs0) = ∅ ++ mklink(m, str)

Rule argument

Additional information

Used simplifier rules: 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% ⊦ ¬ str ∈ ∅; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < 1 ↔ m = 0; (s)% ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ # ∅ = 0; (s)%size-zero: ⊦ # ls ≠ 0 → ls ≠ ∅; (forward) from specification set-basic[alink-set]%⊦ p_ino ∈ dirs ∧ dirs[p_ino] = mkdir(m, md, n, n0, entries) ∧ str ∈ entries → links(entries[str], dirs) ≠ ∅; (s)% ⊦ ls -- alink = ∅ ↔ ls = ∅ ∨ ls = ∅ ++ alink; (ws)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)