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Proof step 200 from proof afs-cons-rename-dir-negdentry (previous step)

# links(entries1[str], dirs0) = dirs0[entries1[str]].nlink, # links(m0, dirs0) = dirs0[m0].nlink, # links(m, dirs0) = dirs0[m].nlink, dirs0[m].nsubdirs = 0, entries1[str] = dirs0[m].entries[str], dirs0[entries1[str]] = mkdir(dirs0[entries1[str]].size, md3, dirs0[entries1[str]].nlink, dirs0[entries1[str]].nsubdirs, entries0), dirs0[m0] = mkdir(dirs0[m0].size, md2, dirs0[m0].nlink, dirs0[m0].nsubdirs, entries), dirs0[m] = mkdir(dirs0[m].size, md4, dirs0[m].nlink, 0, entries1), afs-cons(dirs0, files), str ∈ dirs0[m].entries, m0 ∈ dirs0, m ∈ dirs0, str ∈ entries1, entries1[str] ∈ dirs0, 1 ≤ dirs0[m].size, m0 = m → md1 = md0, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ dirs0[m].size = 0, str0 ∈ dirs0[m0].entries, str0 ∈ entries

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 201:
# links(m, dirs0) = dirs0[m].nlink, # links(m0, dirs0) = dirs0[m0].nlink, # links(entries1[str], dirs0) = m2, dirs0[m].nsubdirs = 0, dirs0[m] = mkdir(dirs0[m].size, md4, dirs0[m].nlink, 0, entries1), dirs0[m0] = mkdir(dirs0[m0].size, md2, dirs0[m0].nlink, dirs0[m0].nsubdirs, entries), dirs0[entries1[str]] = mkdir(m1, md3, m2, m3, entries0), entries1[str] = dirs0[m].entries[str], dirs0[entries1[str]] = mkdir(m1, md, m2, m3, entries2), afs-cons(dirs0, files), entries1[str] ∈ dirs0, str ∈ entries1, m ∈ dirs0, m0 ∈ dirs0, str ∈ dirs0[m].entries, 1 ≤ dirs0[m].size, m0 = m → md1 = md0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ dirs0[m].size = 0, str0 ∈ entries, str0 ∈ dirs0[m0].entries

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[entries1[str]], 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[entries1[str]], m1, md, m2, m3, entries2