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Proof step 501 from proof fsync-pages-keep-abs (previous step)

# buf = VFS_PAGE_SIZE, pcache[datakey(m, n0)] = mkpentry(boolvar1, buf0), pcache[datakey(m, n)] = mkpentry(true, buf), (∅)[m] = mkientry(boolvar0, mkinode(m3, md0, boolvar, m4, m5, m6)), files1[m] = mkfile(m9, md2, m10, content1), files0[m] = mkfile(m9, md2, m10, content), pcache0[datakey(m, n0)] = mkpentry(boolvar2, buf0), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), datakey(m, n0) ∈ pcache0, n0 ∈ content[n, buf] ⊕ mkcontent(m, pcache), n0 ∈ content1 ⊕ mkcontent(m, pcache0), n0 ∈ content ⊕ mkcontent(m, pcache), m ∈ files0, m ∈ files1, datakey(m, n) ∈ pcache, datakey(m, n0) ∈ pcache, ⌊err0⌋ ⊦ buf0 = (content[n, buf] ⊕ mkcontent(m, pcache))[n0], m ∈ icache

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(m, pcache), content[n, buf]] 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(m, pcache), content[n, buf]