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Proof step 546 from proof inv-rename-file-dentry (previous step)

# links(m0, dirs) = m7, dirs[m0] = mkdir(m5, md4, m7, m8, entries1), files[entries1[str0]] = mkfile(m3, md5, # links(entries1[str0], dirs), content0), files[entries[str]] = mkfile(m1, md0, # links(entries[str], dirs), content), dirs[m] = mkdir(m4, md6, # links(m, dirs), m6, entries), entries1[str0] = entries0[str0], dirs[m0] = mkdir(m5, md3, m7, m8, 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 ∈ entries, entries1[str0] ∈ files, entries[str] ∈ files, m0 ∈ dirs, m ∈ dirs, str0 ∈ entries1, str0 ∈ entries0, 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, m7, m8, m5), asynced; err, icache); icache_set#(mkinode(m, md1, true, # links(m, dirs), m6, m4), asynced; err, icache); if true then icache_set#(mkinode(entries[str], md, false, # links(entries[str], dirs), 0, m2), asynced; err, icache); dcache_delete#(m0, mkdentry(str0, entries1[str0]).name; err, dcache); dcache_set#(m, mkdentry(str, entries[str]).name, mkdentry(str, entries[str]); err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced0 → synced(files, icache, pcache))), entries[str] ∈ dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 547:
dirs[m] = mkdir(m4, md6, # links(m, dirs), m6, entries), files[entries[str]] = mkfile(m1, md0, # links(entries[str], dirs), content), files[entries0[str0]] = mkfile(m3, md5, # links(entries0[str0], dirs), content0), dirs[m0] = mkdir(m5, md3, # links(m0, dirs), m8, entries0), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), str0 ∈ entries0, m ∈ dirs, m0 ∈ dirs, entries[str] ∈ files, entries0[str0] ∈ files, str ∈ entries, ¬ entries[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, # links(m0, dirs), m8, m5), asynced; err, icache); icache_set#(mkinode(m, md1, true, # links(m, dirs), m6, m4), asynced; err, icache); if true then icache_set#(mkinode(entries[str], md, false, # links(entries[str], dirs), 0, m2), asynced; err, icache); dcache_delete#(m0, mkdentry(str0, entries0[str0]).name; err, dcache); dcache_set#(m, mkdentry(str, entries[str]).name, mkdentry(str, entries[str]); err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced0 → synced(files, icache, pcache)))

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)