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Proof step 8 from proof inv-crash (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 9:
files[ino] = mkfile(m, md, m0, content), dirs0[ino] = mkdir(m1, md0, m2, m3, entries), afs-cons(dirs0, files), ino ∈ dirs0, name ∈ entries, ROOT_INO ∈ dirs0, ino ∈ dirs0 → m2 = # links(ino, dirs0) ∧ # links(ino, dirs0) ≤ 1 ∧ m1 = # entries ∧ m3 = # subdirs(ino, dirs0), ino ∈ dirs0 ∧ name ∈ entries → entries[name] ∈ dirs0 ∨ entries[name] ∈ files, ino ∈ files → ¬ ino ∈ dirs0 ∧ m0 = # links(ino, dirs0), ino ∈ dirs0 ∧ ino ≠ ROOT_INO ∧ links(ino, dirs0) = ∅ → entries = ∅ ⊦ ino ∈ orphans(dirs0, files), entries[name] ∈ dirs0 ∧ ¬ entries[name] ∈ orphans(dirs0, files), entries[name] ∈ files ∧ ¬ entries[name] ∈ orphans(dirs0, files)

Rule argument

pos: right 1

Additional information

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