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Proof step 192 from proof afs-cons-rename-file-negdentry (previous step)

# links(m0, dirs) = dirs[m0].nlink, dirs[m] = mkdir(m1, md2, # links(m, dirs), m4, entries1), files[entries1[str]] = mkfile(m2, md, # links(entries1[str], dirs), content0), dirs[m0] = mkdir(dirs[m0].size, md3, dirs[m0].nlink, dirs[m0].nsubdirs, entries), afs-cons(dirs, files), str ∈ entries1, m ∈ dirs, entries1[str] ∈ files, 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 193:
# links(m0, dirs) = m5, dirs[m0] = mkdir(m3, md3, m5, m6, entries), files[entries1[str]] = mkfile(m2, md, # links(entries1[str], dirs), content0), dirs[m] = mkdir(m1, md2, # links(m, dirs), m4, entries1), dirs[m0] = mkdir(m3, md4, m5, m6, entries0), afs-cons(dirs, files), m0 ∈ dirs, entries1[str] ∈ files, m ∈ dirs, str ∈ entries1, m0 = m → md1 = md0, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪fail#(; ; err); asynced := ?⟫ true, str0 ∈ entries0, 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[m0], m3, md4, 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: dirs[m0], m3, md4, m5, m6, entries0