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Proof step 58 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), (entries0[str] = ino ⊃ links(entries0[str], dirs0) -- mklink(m, str);links(ino, dirs0)) = ∅, 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), afs-cons(dirs0, files), str ∈ entries0, m ∈ dirs0, ROOT_INO ∈ dirs0, entries0[str] ∈ dirs0, ino ∈ dirs0, # links(ino, dirs0) ≤ 1, name ∈ entries1 → entries1[name] ∈ dirs0 ∨ entries1[name] ∈ files, links(ino, dirs0) = ∅ → entries1 = ∅, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries0[str] = m, entries0[str] = ROOT_INO, entries2 = ∅, ino = ROOT_INO

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: ino = entries0[str]

Additional information

Used simplifier rules: ⊦ afs-cons(dirs, files) → ( links(ino, dirs) = ∅ ↔ (ino ∈ dirs → dirs[ino].nlink = 0) ∧ (ino ∈ files → files[ino].nlink = 0)); (ws)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)% ⊦ mkdir(m, md, m0, m1, entries).nlink = m0; (s)%size-zero-02: ⊦ # ls = 0 → ls = ∅; (forward) from specification set-basic[alink-set]%size-zero-01: ⊦ ls ≠ ∅ → # ls ≠ 0; (forward) from specification set-basic[alink-set]%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)%⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)% ⊦ ¬ str ∈ ∅; (s) Used formulas: ino = entries0[str]