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Proof step 165 from proof afs-cons-rename-file-negdentry (previous step)

# links(m0, dirs0) = dirs0[m0].nlink, # links(m, dirs0) = dirs0[m].nlink, dirs0[m].size = 0, entries0[str] = dirs0[m].entries[str], dirs0[m0] = mkdir(dirs0[m0].size, md3, dirs0[m0].nlink, dirs0[m0].nsubdirs, entries), files[entries0[str]] = mkfile(m2, md, # links(entries0[str], dirs0), content0), dirs0[m] = mkdir(0, md4, dirs0[m].nlink, dirs0[m].nsubdirs, entries0), afs-cons(dirs0, files), str ∈ dirs0[m].entries, m0 ∈ dirs0, entries0[str] ∈ files, m ∈ dirs0, str ∈ entries0, 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 166:
# links(m, dirs0) = m3, # links(m0, dirs0) = dirs0[m0].nlink, dirs0[m] = mkdir(0, md4, m3, m4, entries0), files[entries0[str]] = mkfile(m2, md, # links(entries0[str], dirs0), content0), dirs0[m0] = mkdir(dirs0[m0].size, md3, dirs0[m0].nlink, dirs0[m0].nsubdirs, entries), entries0[str] = entries1[str], dirs0[m] = mkdir(m1, md2, m3, m4, entries1), m1 = 0, afs-cons(dirs0, files), str ∈ entries0, m ∈ dirs0, entries0[str] ∈ files, m0 ∈ dirs0, str ∈ entries1, m0 = m → md1 = md0, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs0) ≠ ∅ ∨ m0 = ROOT_INO ⊦ 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[m], m1, md2, m3, m4, entries1]

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], m1, md2, m3, m4, entries1