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Proof step 93 from proof inv-evict (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 94:
# links(m, dirs) = 0, dcache[key].ino = entries0[str], dirs[m] = mkdir(m0, md, 0, m2, entries), dirs[m3] = mkdir(m1, md0, # links(m3, dirs), m4, entries0), key = dentrykey(m3, str), str = dcache[key].name, 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, 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

spec: key name: elim-03 seq: ⊦ key.dentry? → (m = key.ino ∧ str = key.name ↔ key = dentrykey(m, str)) subst: [key, m, str] → [key, m3, str]

Additional information

Used simplifier rules: ⊦ key.dentry? → (m = key.ino ∧ str = key.name ↔ key = dentrykey(m, str)); (elim) Used terms: key, m3, str