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Proof step 133 from proof overwrite-write-page-dirty (previous step)

((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), icache[ino0] = mkientry(boolvar, mkinode(m2, md0, false, m3, m4, m5)), files[ino0] = mkfile(m6, md1, m7, content0), pcache[datakey(ino0, n)] = mkpentry(boolvar0, buf0), ino ∈ files, ino0 ∈ files, ino ∈ icache, ino0 ∈ icache, datakey(ino0, n) ∈ pcache ⊦ (content0 ⊕ mkcontent(ino0, pcache))[n] = buf0, datakey(ino0, n) = datakey(ino, m), ino0 = ino

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

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;%in-mkcontent: ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache;% ⊦ mkpentry(boolvar, buf).page = buf; (s) Used terms: n, mkcontent(ino0, pcache), content0