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Proof step 73 from proof overwrite-write-page-dirty (previous step)

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

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(ino, pcache), content] 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(ino, pcache), content