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Proof step 238 from proof afs-cons-rename-dir-negdentry (previous step)

# links(m0, dirs0) = dirs0[m0].nlink, dirs0[entries2[str]] = mkdir(m1, md4, # links(entries2[str], dirs0), m4, entries1), dirs0[m0] = mkdir(dirs0[m0].size, md2, dirs0[m0].nlink, dirs0[m0].nsubdirs, entries), dirs0[m] = mkdir(0, md, # links(m, dirs0), m3, entries2), afs-cons(dirs0, files), m0 ∈ dirs0, m ∈ dirs0, entries2[str] ∈ dirs0, str ∈ entries2, m0 = m → md1 = md0, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ str0 ∈ dirs0[m0].entries, str0 ∈ entries

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 239:
# links(m0, dirs0) = m5, dirs0[m] = mkdir(0, md, # links(m, dirs0), m3, entries2), dirs0[m0] = mkdir(m2, md2, m5, m6, entries), dirs0[entries2[str]] = mkdir(m1, md4, # links(entries2[str], dirs0), m4, entries1), dirs0[m0] = mkdir(m2, md3, m5, m6, entries0), afs-cons(dirs0, files), str ∈ entries2, entries2[str] ∈ dirs0, m ∈ dirs0, m0 ∈ dirs0, m0 = m → md1 = md0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ str0 ∈ entries, str0 ∈ entries0

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], m2, md3, m5, 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[m0], m2, md3, m5, m6, entries0