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Proof step 187 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), pcache[datakey(ino0, m)] = mkpentry(boolvar0, buf0), ino0 ∈ icache, ino ∈ files, ino0 ∈ files, ino ∈ icache, m ∈ content1, datakey(ino0, m) ∈ pcache ⊦ (content1 ⊕ mkcontent(ino0, pcache))[m] = buf0, datakey(ino0, m) = datakey(ino, m)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: at-overwrite-content-new seq: ⊦ n ∈ content1 → (content0 ⊕ content1)[n] = content1[n] subst: [n, content1, content0] → [m, mkcontent(ino0, pcache), content1] flags: <all paths>

Additional information

Used simplifier rules: at-overwrite-content-old: ⊦ ¬ n ∈ content1 → (content0 ⊕ content1)[n] = content0[n];%in-mkcontent: ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache;%at-mkcontent: ⊦ mkcontent(ino, pcache)[n] = pcache[datakey(ino, n)].page;%in-mkcontent: ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache;% ⊦ mkpentry(boolvar, buf).page = buf; (s) Used terms: m, mkcontent(ino0, pcache), content1