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Proof step 183 from proof overwrite-write-page-clean (previous step)

((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), files[ino] = mkfile(m2, md0, m3, content0), icache[ino0] = mkientry(boolvar, mkinode(m4, md1, true, m5, m6, m7)), files[ino0] = mkfile(m8, md2, m9, content1), m ∈ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)]), ino0 ∈ icache, ino ∈ files, ino0 ∈ files, ino ∈ icache, m ∈ content1, datakey(ino0, m) ∈ pcache, datakey(ino0, m) ∈ pcache[datakey(ino, m), mkpentry(false, buf)] ⊦ (content1 ⊕ mkcontent(ino0, pcache))[m] = (content1 ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)]))[m], ino0 = ino

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 184:
files[ino0] = mkfile(m8, md2, m9, content1), icache[ino0] = mkientry(boolvar, mkinode(m4, md1, true, m5, m6, m7)), files[ino] = mkfile(m2, md0, m3, content0), ((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), datakey(ino0, m) ∈ pcache, m ∈ content1, ino ∈ icache, ino0 ∈ files, ino ∈ files, ino0 ∈ icache, datakey(ino0, m) ∈ pcache[datakey(ino, m), mkpentry(false, buf)] ⊦ (content1 ⊕ mkcontent(ino0, pcache))[m] = pcache[datakey(ino, m), mkpentry(false, buf)][datakey(ino0, m)].page, ino0 = ino

Rule argument

Additional information

Used simplifier rules: at-overwrite-content-new: ⊦ n ∈ content1 → (content0 ⊕ content1)[n] = content1[n];%at-mkcontent: ⊦ mkcontent(ino, pcache)[n] = pcache[datakey(ino, n)].page;%in-mkcontent: ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache;