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Proof step 58 from proof inv-unlink (previous step)

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

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: ino = m

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)%⊦ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) ∧ str ∈ entries ∧ afs-cons(dirs, files) → (entries[str] ∈ files ↔ ¬ entries[str] ∈ dirs); (ss)% ⊦ str ∈ entries -- str0 ↔ str ≠ str0 ∧ str ∈ entries; (s)% ⊦ str ≠ str0 → (entries -- str0)[str] = entries[str]; (s)% ⊦ # ∅ = 0; (s)% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used formulas: ino = m