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Proof step 162 from proof inv-write_inode (previous step)

dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), pcache[datakey(ino, n)].dirty, afs-cons(dirs, files), afs-cons(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files), synced(dirs, icache, pcache), m ∈ dirs, ino ∈ dirs, datakey(ino, n) ∈ pcache, asynced2 → synced(files, icache, pcache), ino ∈ icache → ¬ icache[ino].dirty, ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty ⊦ m ∈ icache

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 163:
dirs[m] = mkdir(m0, md0, # links(m, dirs), m2, entries), pcache[datakey(ino, n)] = mkpentry(boolvar, buf), boolvar, afs-cons(dirs[m, mkdir(m0, md, # links(m, dirs), m2, entries)], files), afs-cons(dirs, files), synced(dirs, icache, pcache), datakey(ino, n) ∈ pcache, ino ∈ dirs, m ∈ dirs, ino ∈ icache → ¬ icache[ino].dirty, asynced2 → synced(files, icache, pcache), ∀ n. datakey(ino, n) ∈ pcache → ¬ pcache[datakey(ino, n)].dirty ⊦ m ∈ icache

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