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Proof step 87 from proof inv-evict (previous step)

# links(m, dirs) = 0, dirs[m] = mkdir(m0, md, 0, m2, entries), afs-cons(dirs -- m, files), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), synced(dirs, icache, pcache), key ∈ dcache, m ∈ dirs, asynced1 → synced(files, icache, pcache) ⊦ m = ROOT_INO, key.dentry? ∧ key.name = dcache[key].name ∧ key.ino ≠ m ∧ key.ino ∈ dirs ∧ (links(key.ino, dirs -- m) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ (dcache[key].ino ≠ m ∧ dcache[key].ino ∈ dirs ∨ dcache[key].ino ∈ files) ∧ dcache[key].name ∈ dirs[key.ino].entries ∧ dcache[key].ino = dirs[key.ino].entries[dcache[key].name] ∧ dcache[key].dentry?

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 88:
# links(m, dirs) = 0, dirs[m] = mkdir(m0, md, 0, m2, entries), dirs[key.ino] = mkdir(m1, md0, m3, m4, entries0), afs-cons(dirs, files), afs-cons(dirs -- m, files), dcache-cons(dcache, dirs, files), synced(dirs, icache, pcache), m ∈ dirs, key ∈ dcache, asynced1 → synced(files, icache, pcache) ⊦ m = ROOT_INO, key.dentry? ∧ key.name = dcache[key].name ∧ key.ino ≠ m ∧ key.ino ∈ dirs ∧ (links(key.ino, dirs -- m) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ (dcache[key].ino ≠ m ∧ dcache[key].ino ∈ dirs ∨ dcache[key].ino ∈ files) ∧ dcache[key].name ∈ entries0 ∧ dcache[key].ino = entries0[dcache[key].name] ∧ dcache[key].dentry?

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [dirs[key.ino], m1, md0, m3, m4, entries0]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: dirs[key.ino], m1, md0, m3, m4, entries0