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Proof step 210 from proof afs-cons-rename-file-dentry (previous step)

# links(m, dirs0) = dirs0[m].nlink, entries[str] = dirs0[m].entries[str], dirs0[m] = mkdir(dirs0[m].size, md5, dirs0[m].nlink, dirs0[m].nsubdirs, entries), files[entries[str]] = mkfile(m2, md, # links(entries[str], dirs0), content1), files[entries1[str0]] = mkfile(m1, md0, # links(entries1[str0], dirs0), content), dirs0[m0] = mkdir(0, md3, # links(m0, dirs0), m5, entries1), afs-cons(dirs0, files), str ∈ dirs0[m].entries, str ∈ entries, str0 ∈ entries1, m ∈ dirs0, m0 ∈ dirs0, entries[str] ∈ files, entries1[str0] ∈ files, m = m0 → md1 = md2, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ entries[str] ∈ dirs0, 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 211:
# links(m, dirs0) = m4, dirs0[m0] = mkdir(0, md3, # links(m0, dirs0), m5, entries1), files[entries1[str0]] = mkfile(m1, md0, # links(entries1[str0], dirs0), content), files[entries[str]] = mkfile(m2, md, # links(entries[str], dirs0), content1), dirs0[m] = mkdir(m3, md5, m4, m6, entries), entries[str] = entries0[str], dirs0[m] = mkdir(m3, md4, m4, m6, entries0), afs-cons(dirs0, files), entries1[str0] ∈ files, entries[str] ∈ files, m0 ∈ dirs0, m ∈ dirs0, str0 ∈ entries1, str ∈ entries, str ∈ entries0, m = m0 → md1 = md2, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ entries[str] ∈ dirs0, 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[m], m3, md4, m4, m6, entries0]

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[m], m3, md4, m4, m6, entries0