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Proof step 47 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), synced(files, icache, pcache), ino ∈ files, m ∈ dirs, ino ∈ icache → ¬ icache[ino].dirty, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty ⊦ m = ROOT_INO, (ino ≠ m ∧ ino ∈ icache → ¬ icache[ino].dirty) ∧ (datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 48:
# links(m, dirs) = 0, dirs[m] = mkdir(m0, md, 0, m2, entries), pcache[datakey(ino, n)] = mkpentry(boolvar, buf), afs-cons(dirs, files), afs-cons(dirs -- m, files), synced(files, icache, pcache), m ∈ dirs, ino ∈ files, ino ∈ icache → ¬ icache[ino].dirty, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty ⊦ m = ROOT_INO, (ino ≠ m ∧ ino ∈ icache → ¬ icache[ino].dirty) ∧ (datakey(ino, n) ∈ pcache → ¬ boolvar)

Rule argument

spec: pcache-entry name: elim seq: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf) subst: [pe, boolvar, buf] → [pcache[datakey(ino, n)], boolvar, buf]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ pe.dirty) ∧ buf = pe.page ↔ pe = mkpentry(boolvar, buf); (elim) Used terms: pcache[datakey(ino, n)], boolvar, buf