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Proof step 234 from proof overwrite-write-page-dirty (previous step)

files[ino] = mkfile(m2, md0, m3, content0), ino ∈ files ⊦ buf = (content0 ⊕ mkcontent(ino, pcache[datakey(ino, m), mkpentry(true, buf)]))[m], ino ∈ icache

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(ino, pcache[datakey(ino, m), mkpentry(true, buf)]), content0] 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;% ⊦ pcache[key, pe][key] = pe; (s)% ⊦ mkpentry(boolvar, buf).page = buf; (s)% ⊦ key ∈ pcache[key0, pe] ↔ key = key0 ∨ key ∈ pcache; (ws) Used terms: m, mkcontent(ino, pcache[datakey(ino, m), mkpentry(true, buf)]), content0