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Proof step 291 from proof afs-cons-rename-file-dentry (previous step)

# links(m, dirs) = dirs[m].nlink, entries[str] = dirs[m].entries[str], dirs[m0] = mkdir(m1, md3, # links(m0, dirs), m5, entries1), files[entries1[str0]] = mkfile(m2, md, # links(entries1[str0], dirs), content1), files[entries[str]] = mkfile(m3, md0, # links(entries[str], dirs), content0), dirs[m] = mkdir(dirs[m].size, md5, dirs[m].nlink, dirs[m].nsubdirs, entries), afs-cons(dirs, files), str ∈ dirs[m].entries, entries1[str0] ∈ files, entries[str] ∈ files, m0 ∈ dirs, m ∈ dirs, str0 ∈ entries1, str ∈ entries, ¬ entries[str] ∈ dirs, m = m0 → md1 = md2, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪fail#(; ; err); asynced := ?⟫ true

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 292:
# links(m, dirs) = m6, dirs[m] = mkdir(m4, md5, m6, m7, entries), files[entries[str]] = mkfile(m3, md0, # links(entries[str], dirs), content0), files[entries1[str0]] = mkfile(m2, md, # links(entries1[str0], dirs), content1), dirs[m0] = mkdir(m1, md3, # links(m0, dirs), m5, entries1), entries[str] = entries0[str], dirs[m] = mkdir(m4, md4, m6, m7, entries0), afs-cons(dirs, files), str ∈ entries, str0 ∈ entries1, m ∈ dirs, m0 ∈ dirs, entries[str] ∈ files, entries1[str0] ∈ files, str ∈ entries0, m = m0 → md1 = md2, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO ⊦ ⟪fail#(; ; err); asynced := ?⟫ true, entries[str] ∈ dirs

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], m4, md4, m6, m7, 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[m], m4, md4, m6, m7, entries0