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Proof step 234 from proof inv-link (previous step)

# links(m, dirs) = dirs[m].nlink, entries1[str] = dirs[ino2].entries[str], dirs[ino1] = mkdir(m5, md2, # links(ino1, dirs), m10, entries1), entries[str] = entries1[str], dirs[ino0] = mkdir(m2, md1, # links(ino0, dirs), m8, entries), entries0[str] = entries1[str], files[entries1[str]] = mkfile(m0, md6, # links(entries1[str], dirs), content0), dirs[m] = mkdir(dirs[m].size, md4, dirs[m].nlink, dirs[m].nsubdirs, entries2), dirs[ino] = mkdir(m4, md3, # links(ino, dirs), m6, 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[ino2].entries, ino2 ∈ dirs, str ∈ entries1, ino1 ∈ dirs, str ∈ entries, ino0 ∈ dirs, ino ∈ dirs, str ∈ entries0, m ∈ dirs, entries1[str] ∈ files, ¬ str0 ∈ entries2, ¬ str0 ∈ dirs[m].entries, asynced1 → synced(files, icache, pcache), links(ino2, dirs) ≠ ∅ ∨ ino2 = ROOT_INO, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [fail#(; ; err); asynced := ?] ⟪if err = ESUCCESS then let asynced = false in {icache_set#(mkinode(m, md, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), asynced; err, icache); icache_set#(mkinode(entries1[str], md0, false, # links(entries1[str], dirs), 0, m3), asynced; err, icache); dcache_set#(m, str0, negdentry(str0); err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced1 → synced(files, icache, pcache)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 235:
# links(m, dirs) = m7, dirs[ino] = mkdir(m4, md3, # links(ino, dirs), m6, entries0), dirs[m] = mkdir(m1, md4, m7, m9, entries2), files[entries1[str]] = mkfile(m0, md6, # links(entries1[str], dirs), content0), entries0[str] = entries1[str], dirs[ino0] = mkdir(m2, md1, # links(ino0, dirs), m8, entries), entries[str] = entries1[str], dirs[ino1] = mkdir(m5, md2, # links(ino1, dirs), m10, entries1), entries1[str] = dirs[ino2].entries[str], dirs[m] = mkdir(m1, md5, m7, m9, entries3), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), entries1[str] ∈ files, m ∈ dirs, str ∈ entries0, ino ∈ dirs, ino0 ∈ dirs, str ∈ entries, ino1 ∈ dirs, str ∈ entries1, ino2 ∈ dirs, str ∈ dirs[ino2].entries, asynced1 → synced(files, icache, pcache), links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, links(ino0, dirs) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino2, dirs) ≠ ∅ ∨ ino2 = ROOT_INO ⊦ [fail#(; ; err); asynced := ?] ⟪if err = ESUCCESS then let asynced = false in {icache_set#(mkinode(m, md, true, m7, m9, m1), asynced; err, icache); icache_set#(mkinode(entries1[str], md0, false, # links(entries1[str], dirs), 0, m3), asynced; err, icache); dcache_set#(m, str0, negdentry(str0); err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced1 → synced(files, icache, pcache))), str0 ∈ entries2, str0 ∈ entries3

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, md5, m7, m9, entries3]

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, md5, m7, m9, entries3