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Proof step 302 from proof inv-rename-file-negdentry (previous step)

# links(m0, dirs) = dirs[m0].nlink, # links(m, dirs) = dirs[m].nlink, entries1[str] = dirs[m].entries[str], dirs[m] = mkdir(dirs[m].size, md2, dirs[m].nlink, dirs[m].nsubdirs, entries1), files[entries1[str]] = mkfile(m2, md, # links(entries1[str], dirs), content0), dirs[m0] = mkdir(dirs[m0].size, md5, dirs[m0].nlink, dirs[m0].nsubdirs, entries0), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), str ∈ dirs[m].entries, str ∈ entries1, m ∈ dirs, entries1[str] ∈ files, m0 ∈ dirs, ¬ str0 ∈ entries0, ¬ str0 ∈ dirs[m0].entries, asynced0 → synced(files, icache, pcache), m0 = m → md1 = md0, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO ⊦ [fail#(; ; err); asynced := ?] ⟪if err = ESUCCESS then let asynced = false in {icache_set#(mkinode(m, md0, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), asynced; err, icache); icache_set#(mkinode(m0, md1, true, # links(m0, dirs), dirs[m0].nsubdirs, dirs[m0].size), asynced; err, icache); skip; dcache_delete#(m, mkdentry(str, entries1[str]).name; err, dcache); dcache_set#(m0, str0, negdentry(str0); err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced0 → synced(files, icache, pcache)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 303:
# links(m, dirs) = m3, # links(m0, dirs) = dirs[m0].nlink, dirs[m0] = mkdir(dirs[m0].size, md5, dirs[m0].nlink, dirs[m0].nsubdirs, entries0), files[entries1[str]] = mkfile(m2, md, # links(entries1[str], dirs), content0), dirs[m] = mkdir(m1, md2, m3, m4, entries1), entries1[str] = entries[str], dirs[m] = mkdir(m1, md3, m3, m4, entries), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m0 ∈ dirs, entries1[str] ∈ files, m ∈ dirs, str ∈ entries1, str ∈ entries, m0 = m → md1 = md0, asynced0 → synced(files, icache, pcache), links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [fail#(; ; err); asynced := ?] ⟪if err = ESUCCESS then let asynced = false in {icache_set#(mkinode(m, md0, true, m3, m4, m1), asynced; err, icache); icache_set#(mkinode(m0, md1, true, # links(m0, dirs), dirs[m0].nsubdirs, dirs[m0].size), asynced; err, icache); skip; dcache_delete#(m, mkdentry(str, entries1[str]).name; err, dcache); dcache_set#(m0, str0, negdentry(str0); err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced0 → synced(files, icache, pcache))), str0 ∈ entries0, str0 ∈ dirs[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] → [dirs[m], m1, md3, m3, m4, entries]

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, md3, m3, m4, entries