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Proof step 45 from proof inv-recover (previous step)

dirs0[ino] = mkdir(m1, md0, m2, m3, entries), files1[ino] = mkfile(m, md, m0, content), afs-cons(dirs0, files1) ⊦ (ino ∈ dirs0 ∧ ¬ ino ∈ orphans(dirs0, files1) ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries = ∅) ∧ ( ino ∈ dirs0 ∧ ¬ ino ∈ orphans(dirs0, files1) → m2 = # links(ino, dirs0) ∧ # links(ino, dirs0) ≤ 1 ∧ m1 = # entries ∧ m3 = # subdirs(ino, dirs0)) ∧ (ino ∈ files1 ∧ ¬ ino ∈ orphans(dirs0, files1) → ¬ ino ∈ dirs0 ∧ m0 = # links(ino, dirs0)) ∧ ( ino ∈ dirs0 ∧ ¬ ino ∈ orphans(dirs0, files1) ∧ name ∈ entries → entries[name] ∈ dirs0 ∧ ¬ entries[name] ∈ orphans(dirs0, files1) ∨ entries[name] ∈ files1 ∧ ¬ entries[name] ∈ orphans(dirs0, files1))

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 46:
files1[ino] = mkfile(m, md, m0, content), dirs0[ino] = mkdir(m1, md0, m2, m3, entries), afs-cons(dirs0, files1), ino ∈ dirs0 ⊦ (ino ∈ dirs0 ∧ ¬ ino ∈ orphans(dirs0, files1) ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries = ∅) ∧ ( ino ∈ dirs0 ∧ ¬ ino ∈ orphans(dirs0, files1) → m2 = # links(ino, dirs0) ∧ # links(ino, dirs0) ≤ 1 ∧ m1 = # entries ∧ m3 = # subdirs(ino, dirs0)) ∧ (ino ∈ files1 ∧ ¬ ino ∈ orphans(dirs0, files1) → ¬ ino ∈ dirs0 ∧ m0 = # links(ino, dirs0)) ∧ ( ino ∈ dirs0 ∧ ¬ ino ∈ orphans(dirs0, files1) ∧ name ∈ entries → entries[name] ∈ dirs0 ∧ ¬ entries[name] ∈ orphans(dirs0, files1) ∨ entries[name] ∈ files1 ∧ ¬ entries[name] ∈ orphans(dirs0, files1))

Rule argument

fma: ino ∈ dirs0

Additional information

Used simplifier rules: afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base Used formulas: ino ∈ dirs0