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Proof step 96 from proof inv-evict (previous step)

# links(m, dirs) = 0, dirs[m] = mkdir(m0, md, 0, m2, entries), dirs[m3] = mkdir(m1, md0, # links(m3, dirs), m4, entries0), dcache[key] = mkdentry(str, m5), key = dentrykey(m3, str), m5 = entries0[str], dcache[key].dentry?, key.dentry?, afs-cons(dirs, files), afs-cons(dirs -- m, files), synced(dirs, icache, pcache), str ∈ entries0, m ∈ dirs, key ∈ dcache, m3 ∈ dirs, asynced1 → 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?, links(m3, dirs) ≠ ∅ ∨ m3 = ROOT_INO, m5 ∈ dirs ∨ m5 ∈ files ⊦ m = ROOT_INO, m3 ≠ m ∧ (links(m3, dirs -- m) ≠ ∅ ∨ m3 = ROOT_INO) ∧ (m5 ≠ m ∧ m5 ∈ dirs ∨ m5 ∈ files)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 97:
# links(m, dirs) = 0, dirs[m] = mkdir(m0, md, 0, m2, entries), dirs[m3] = mkdir(m1, md0, # links(m3, dirs), m4, entries0), dcache[dentrykey(m3, str)] = mkdentry(str, entries0[str]), afs-cons(dirs, files), afs-cons(dirs -- m, files), synced(dirs, icache, pcache), str ∈ entries0, m ∈ dirs, dentrykey(m3, str) ∈ dcache, m3 ∈ dirs, asynced1 → 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?, links(m3, dirs) ≠ ∅ ∨ m3 = ROOT_INO, entries0[str] ∈ dirs ∨ entries0[str] ∈ files ⊦ m = ROOT_INO, m3 ≠ m ∧ (links(m3, dirs -- m) ≠ ∅ ∨ m3 = ROOT_INO) ∧ (entries0[str] ≠ m ∧ entries0[str] ∈ dirs ∨ entries0[str] ∈ files)

Rule argument

Additional information

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