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Proof step 391 from proof inv-write_inode (previous step)

afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), synced(dirs, icache, pcache), synced(files, icache, pcache), key ∈ dcache, m ∈ files ⊦ m ∈ icache, key.dentry? ∧ key.name = dcache[key].name ∧ key.ino ∈ dirs ∧ (links(key.ino, dirs) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ (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 392:
dirs[key.ino] = mkdir(m0, md0, m1, m3, entries), afs-cons(dirs, files), afs-cons(dirs, files[m, (files[m].meta:= md).size:= m2]), dcache-cons(dcache, dirs, files), synced(files, icache, pcache), synced(dirs, icache, pcache), m ∈ files, key ∈ dcache ⊦ m ∈ icache, key.dentry? ∧ key.name = dcache[key].name ∧ key.ino ∈ dirs ∧ (links(key.ino, dirs) ≠ ∅ ∨ key.ino = ROOT_INO) ∧ (dcache[key].ino ∈ dirs ∨ dcache[key].ino ∈ files) ∧ dcache[key].name ∈ entries ∧ dcache[key].ino = entries[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], m0, md0, m1, m3, entries]

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], m0, md0, m1, m3, entries