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Proof step 56 from proof inv-unlink (previous step)

# links(entries0[str], dirs0) = m1 + 1, (ino = entries0[str] ⊃ mkfile(m0, md1, m1, content);mkfile(m4, md, m5, content0)) = mkfile(m6, md0, m7, content1), (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), files0[ino] = mkfile(m4, md, m5, content0), files0[entries0[str]] = mkfile(m0, md1, m1 + 1, content), dirs0[m] = mkdir(m2 + 1, md2, # links(m, dirs0), m3, entries0), dirs0[ino] = mkdir(# entries, md3, # links(ino, dirs0), # subdirs(ino, dirs0), entries), afs-cons(dirs0, files0), ino ∈ dirs0, name ∈ entries1, m ∈ dirs0, str ∈ entries0, entries0[str] ∈ files0, ROOT_INO ∈ dirs0, # links(ino, dirs0) ≤ 1, ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries = ∅, name ∈ entries → entries[name] ∈ dirs0 ∨ entries[name] ∈ files0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries1[name] ∈ dirs0, entries1[name] ∈ files0

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 57:
# 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), (ino = entries0[str] ⊃ mkfile(m0, md1, m1, content);mkfile(m4, md, m5, content0)) = mkfile(m6, md0, m7, content1), 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

Rule argument

fma: ino = entries0[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)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s) Used formulas: ino = entries0[str]