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Proof step 308 from proof afs-cons-rename-dir-dentry (previous step)

# links(entries1[str0], dirs0) = dirs0[entries1[str0]].nlink, # links(m, dirs0) = dirs0[m].nlink, # links(m0, dirs0) = dirs0[m0].nlink, # links(entries[str], dirs0) = dirs0[entries[str]].nlink, dirs0[entries[str]].entries = ∅, dirs0[m0].size = 0, entries1[str0] = dirs0[m0].entries[str0], entries[str] = dirs0[m].entries[str], dirs0[entries1[str0]] = mkdir(dirs0[entries1[str0]].size, md5, dirs0[entries1[str0]].nlink, dirs0[entries1[str0]].nsubdirs, entries0), dirs0[entries[str]] = mkdir(dirs0[entries[str]].size, md3, dirs0[entries[str]].nlink, dirs0[entries[str]].nsubdirs, ∅), dirs0[m] = mkdir(dirs0[m].size, md4, dirs0[m].nlink, dirs0[m].nsubdirs, entries), dirs0[m0] = mkdir(0, md6, dirs0[m0].nlink, dirs0[m0].nsubdirs, entries1), afs-cons(dirs0, files), str0 ∈ dirs0[m0].entries, str ∈ dirs0[m].entries, str ∈ entries, str0 ∈ entries1, entries[str] ∈ dirs0, entries1[str0] ∈ dirs0, m ∈ dirs0, m0 ∈ dirs0, m = m0 → md1 = md2, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ entries[str] = ROOT_INO, m0 = m ∧ mkdentry(str, entries[str]) = mkdentry(str0, entries1[str0])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 309:
# links(entries[str], dirs0) = dirs0[entries[str]].nlink, # links(m0, dirs0) = m2, # links(m, dirs0) = dirs0[m].nlink, # links(entries1[str0], dirs0) = dirs0[entries1[str0]].nlink, dirs0[entries[str]].entries = ∅, dirs0[m0] = mkdir(0, md6, m2, m3, entries1), dirs0[m] = mkdir(dirs0[m].size, md4, dirs0[m].nlink, dirs0[m].nsubdirs, entries), dirs0[entries[str]] = mkdir(dirs0[entries[str]].size, md3, dirs0[entries[str]].nlink, dirs0[entries[str]].nsubdirs, ∅), dirs0[entries1[str0]] = mkdir(dirs0[entries1[str0]].size, md5, dirs0[entries1[str0]].nlink, dirs0[entries1[str0]].nsubdirs, entries0), entries[str] = dirs0[m].entries[str], entries1[str0] = entries2[str0], dirs0[m0] = mkdir(m1, md, m2, m3, entries2), m1 = 0, afs-cons(dirs0, files), m0 ∈ dirs0, m ∈ dirs0, entries1[str0] ∈ dirs0, entries[str] ∈ dirs0, str0 ∈ entries1, str ∈ entries, str ∈ dirs0[m].entries, str0 ∈ entries2, m = m0 → md1 = md2, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries[str] = ROOT_INO, m0 = m ∧ mkdentry(str, entries[str]) = mkdentry(str0, entries1[str0])

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] → [dirs0[m0], m1, md, m2, m3, entries2]

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: dirs0[m0], m1, md, m2, m3, entries2