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Proof step 259 from proof afs-cons-rename-dir-negdentry (previous step)

# links(entries1[str], dirs) = dirs[entries1[str]].nlink, # links(m0, dirs) = dirs[m0].nlink, # links(m, dirs) = dirs[m].nlink, entries1[str] = dirs[m].entries[str], dirs[m] = mkdir(dirs[m].size, md4, dirs[m].nlink, dirs[m].nsubdirs, entries1), dirs[m0] = mkdir(dirs[m0].size, md2, dirs[m0].nlink, dirs[m0].nsubdirs, entries), dirs[entries1[str]] = mkdir(dirs[entries1[str]].size, md3, dirs[entries1[str]].nlink, dirs[entries1[str]].nsubdirs, entries0), afs-cons(dirs, files), str ∈ dirs[m].entries, str ∈ entries1, entries1[str] ∈ dirs, m ∈ dirs, m0 ∈ dirs, ¬ str0 ∈ dirs[m0].entries, ¬ str0 ∈ entries, m0 = m → md1 = md0, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪fail#(; ; err); asynced := ?⟫ true

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 260:
# links(m, dirs) = m2, # links(m0, dirs) = dirs[m0].nlink, # links(entries1[str], dirs) = dirs[entries1[str]].nlink, dirs[entries1[str]] = mkdir(dirs[entries1[str]].size, md3, dirs[entries1[str]].nlink, dirs[entries1[str]].nsubdirs, entries0), dirs[m0] = mkdir(dirs[m0].size, md2, dirs[m0].nlink, dirs[m0].nsubdirs, entries), dirs[m] = mkdir(m1, md4, m2, m3, entries1), entries1[str] = entries2[str], dirs[m] = mkdir(m1, md, m2, m3, entries2), afs-cons(dirs, files), m0 ∈ dirs, m ∈ dirs, entries1[str] ∈ dirs, str ∈ entries1, str ∈ entries2, m0 = m → md1 = md0, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪fail#(; ; err); asynced := ?⟫ true, str0 ∈ dirs[m0].entries, str0 ∈ 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] → [dirs[m], 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: dirs[m], m1, md, m2, m3, entries2