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Proof step 214 from proof inv-unlink (previous step)

# links(entries[str], dirs) = m2, # links(m, dirs) = dirs[m].nlink, dirs[m] = mkdir(dirs[m].size, md3, dirs[m].nlink, dirs[m].nsubdirs, entries), files[entries[str]] = mkfile(m0, md2, m2, content), entries[str] = dirs[m].entries[str], files[entries[str]] = mkfile(m1, md1, m2, content0), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ dirs, str ∈ entries, entries[str] ∈ files, str ∈ dirs[m].entries, asynced1 → synced(files, icache, pcache), links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [fail#(; ; err); asynced := ?] ⟪if err = ESUCCESS then let asynced = false in {icache_set#(mkinode(entries[str], md0, false, m2, 0, m3), asynced; err, icache); icache_set#(mkinode(m, md, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), asynced; err, icache); dcache_delete#(m, mkdentry(str, entries[str]).name; err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced1 → synced(files, icache, pcache)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 215:
# links(m, dirs) = dirs[m].nlink, entries[str] = dirs[m].entries[str], files[entries[str]] = mkfile(m1, md1, # links(entries[str], dirs), content0), dirs[m] = mkdir(dirs[m].size, md3, dirs[m].nlink, dirs[m].nsubdirs, 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 ∈ dirs[m].entries, entries[str] ∈ files, str ∈ entries, m ∈ dirs, asynced1 → synced(files, icache, pcache), links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [fail#(; ; err); asynced := ?] ⟪if err = ESUCCESS then let asynced = false in {icache_set#(mkinode(entries[str], md0, false, # links(entries[str], dirs), 0, m3), asynced; err, icache); icache_set#(mkinode(m, md, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), asynced; err, icache); dcache_delete#(m, mkdentry(str, entries[str]).name; err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced1 → synced(files, icache, pcache)))

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)