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Proof step 196 from proof inv-write_inode (previous step)

(m5 = m ⊃ mkdir(m0, md, # links(m, dirs), m2, entries);dirs[m5]) = mkdir(m1, md1, m3, m4, entries0), dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), dcache[key] = mkdentry(str, m6), key = dentrykey(m5, str), m6 = dirs[m5].entries[str], dcache[key].dentry?, key.dentry?, afs-cons(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files), afs-cons(dirs, files), synced(dirs, icache, pcache), str ∈ dirs[m5].entries, m5 ∈ dirs, key ∈ dcache, m ∈ dirs, asynced2 → synced(files, icache, pcache), ∀ key0. key0 ∈ dcache → key0.dentry? ∧ key0.name = dcache[key0].name ∧ key0.ino ∈ dirs ∧ (links(key0.ino, dirs) ≠ ∅ ∨ key0.ino = ROOT_INO) ∧ (dcache[key0].ino ∈ dirs ∨ dcache[key0].ino ∈ files) ∧ dcache[key0].name ∈ dirs[key0.ino].entries ∧ dcache[key0].ino = dirs[key0.ino].entries[dcache[key0].name] ∧ dcache[key0].dentry?, m6 ∈ dirs ∨ m6 ∈ files, links(m5, dirs) ≠ ∅ ∨ m5 = ROOT_INO ⊦ m ∈ icache, str ∈ entries0 ∧ m6 = entries0[str]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 197:
(m5 = m ⊃ mkdir(m0, md, # links(m, dirs), m2, entries);dirs[m5]) = mkdir(m1, md1, m3, m4, entries0), dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), dcache[dentrykey(m5, str)] = mkdentry(str, dirs[m5].entries[str]), afs-cons(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files), afs-cons(dirs, files), synced(dirs, icache, pcache), str ∈ dirs[m5].entries, m5 ∈ dirs, dentrykey(m5, str) ∈ dcache, m ∈ dirs, asynced2 → synced(files, icache, pcache), ∀ key0. key0 ∈ dcache → key0.dentry? ∧ key0.name = dcache[key0].name ∧ key0.ino ∈ dirs ∧ (links(key0.ino, dirs) ≠ ∅ ∨ key0.ino = ROOT_INO) ∧ (dcache[key0].ino ∈ dirs ∨ dcache[key0].ino ∈ files) ∧ dcache[key0].name ∈ dirs[key0.ino].entries ∧ dcache[key0].ino = dirs[key0.ino].entries[dcache[key0].name] ∧ dcache[key0].dentry?, dirs[m5].entries[str] ∈ dirs ∨ dirs[m5].entries[str] ∈ files, links(m5, dirs) ≠ ∅ ∨ m5 = ROOT_INO ⊦ m ∈ icache, str ∈ entries0 ∧ dirs[m5].entries[str] = entries0[str]

Rule argument

Additional information

Used simplifier rules: ⊦ mkdentry(str, m).dentry?; (s)% ⊦ dentrykey(m, str).dentry?; (s)