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Proof step 13 from proof orphans-del-file (previous step)

# links(ino, dirs) = 0, files[ino] = mkfile(n, md, 0, content), files[ino0] = mkfile(m, md0, m0, content0), afs-cons(dirs, files), ino ∈ files, ino0 ∈ files → m0 = 0, ino0 ∈ dirs → dirs[ino0].nlink = 0, ino0 ∈ dirs ∨ ino0 ≠ ino ∧ ino0 ∈ files ⊦ ino0 = ROOT_INO, ino ∈ dirs, ino0 ≠ ino ∧ (ino0 ∈ dirs ∨ ino0 ∈ files)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 14:
# links(ino, dirs) = 0, files[ino0] = mkfile(m, md0, m0, content0), files[ino] = mkfile(n, md, 0, content), dirs[ino0] = mkdir(m1, md1, m2, m3, entries), afs-cons(dirs, files), ino ∈ files, ino0 ∈ dirs → m2 = 0, ino0 ∈ files → m0 = 0, ino0 ∈ dirs ∨ ino0 ≠ ino ∧ ino0 ∈ files ⊦ ino0 = ROOT_INO, ino ∈ dirs, ino0 ≠ ino ∧ (ino0 ∈ dirs ∨ ino0 ∈ files)

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [dirs[ino0], m1, md1, m2, m3, entries]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: dirs[ino0], m1, md1, m2, m3, entries