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Proof step 543 from proof inv-rename-file-dentry (previous step)

# links(m, dirs) = dirs[m].nlink, # links(m0, dirs) = dirs[m0].nlink, entries1[str0] = dirs[m0].entries[str0], entries0[str] = dirs[m].entries[str], dirs[m] = mkdir(dirs[m].size, md3, dirs[m].nlink, dirs[m].nsubdirs, entries0), files[entries0[str]] = mkfile(m1, md0, # links(entries0[str], dirs), content), files[entries1[str0]] = mkfile(m3, md5, # links(entries1[str0], dirs), content0), dirs[m0] = mkdir(dirs[m0].size, md4, dirs[m0].nlink, dirs[m0].nsubdirs, entries1), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), str0 ∈ dirs[m0].entries, str ∈ dirs[m].entries, str0 ∈ entries1, m ∈ dirs, m0 ∈ dirs, entries0[str] ∈ files, entries1[str0] ∈ files, str ∈ entries0, ¬ entries0[str] ∈ dirs, asynced0 → synced(files, icache, pcache), m = m0 → md1 = md2, 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(m0, md2, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size), asynced; err, icache); icache_set#(mkinode(m, md1, true, # links(m, dirs), dirs[m].nsubdirs, dirs[m].size), asynced; err, icache); if true then icache_set#(mkinode(entries0[str], md, false, # links(entries0[str], dirs), 0, m2), asynced; err, icache); dcache_delete#(m0, mkdentry(str0, entries1[str0]).name; err, dcache); dcache_set#(m, mkdentry(str, entries0[str]).name, mkdentry(str, entries0[str]); 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 544:
# links(m0, dirs) = dirs[m0].nlink, # links(m, dirs) = m5, dirs[m0] = mkdir(dirs[m0].size, md4, dirs[m0].nlink, dirs[m0].nsubdirs, entries1), files[entries1[str0]] = mkfile(m3, md5, # links(entries1[str0], dirs), content0), files[entries0[str]] = mkfile(m1, md0, # links(entries0[str], dirs), content), dirs[m] = mkdir(m4, md3, m5, m6, entries0), entries0[str] = entries[str], entries1[str0] = dirs[m0].entries[str0], dirs[m] = mkdir(m4, md6, m5, m6, entries), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), str ∈ entries0, entries1[str0] ∈ files, entries0[str] ∈ files, m0 ∈ dirs, m ∈ dirs, str0 ∈ entries1, str ∈ entries, str0 ∈ dirs[m0].entries, m = m0 → md1 = md2, 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(m0, md2, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size), asynced; err, icache); icache_set#(mkinode(m, md1, true, # links(m, dirs), m6, m4), asynced; err, icache); if true then icache_set#(mkinode(entries0[str], md, false, # links(entries0[str], dirs), 0, m2), asynced; err, icache); dcache_delete#(m0, mkdentry(str0, entries1[str0]).name; err, dcache); dcache_set#(m, mkdentry(str, entries0[str]).name, mkdentry(str, entries0[str]); err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced0 → synced(files, icache, pcache))), entries0[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, md6, m5, m6, 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], m4, md6, m5, m6, entries