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Proof step 268 from proof fsync-pages-keep-abs (previous step)

# buf = VFS_PAGE_SIZE, pcache0[datakey(ino, n0)] = mkpentry(boolvar, content2[n0]), icache[ino] = mkientry(boolvar0, mkinode(m3, md0, true, m4, m5, m6)), pcache[datakey(m, n)] = mkpentry(true, buf), files0[m] = mkfile(m0, md, m1, content), files0[ino] = mkfile(m7, md1, m8, content2), files1[ino] = mkfile(m7, md1, m8, content1), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), ino ∈ icache, m ∈ files0, datakey(m, n) ∈ pcache, ino ∈ files1, ino ∈ files0, datakey(ino, n0) ∈ pcache0, n0 ∈ content1 ⊕ mkcontent(ino, pcache0), n0 ∈ content2, ∀ ino0. (ino0 ∈ files0 ↔ ino0 ∈ files1) ∧ (ino0 ∈ files0 → ((files0 ⊕ pcache) ⊕ icache)[ino0] = ((files1 ⊕ pcache0) ⊕ icache)[ino0]) ⊦ (content1 ⊕ mkcontent(ino, pcache0))[n0] = content2[n0], datakey(ino, n0) = datakey(m, n), ino = m, datakey(ino, n0) ∈ pcache

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: cache-base name: at-overwrite-content-new seq: ⊦ n ∈ content1 → (content0 ⊕ content1)[n] = content1[n] subst: [n, content1, content0] → [n0, mkcontent(ino, pcache0), content1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ mkcontent(ino, pcache)[n] = pcache[datakey(ino, n)].page; (s)% ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache; (s)% ⊦ mkpentry(boolvar, buf).page = buf; (s)% ⊦ ¬ n ∈ content1 → (content0 ⊕ content1)[n] = content0[n]; (s)% ⊦ n ∈ content0 ⊕ content1 ↔ n ∈ content0 ∨ n ∈ content1; (ws)% ⊦ ¬ key ∈ pcache → pcache[key] = (∅)[key]; (s) Used terms: n0, mkcontent(ino, pcache0), content1