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Proof step 22 from proof pcache-overwrite-read-page (previous step)

files[ino0] = mkfile(m1, md0, m2, content0), files[ino] = mkfile(m, md, m0, content), n ∈ content, ino ∈ files, ino0 ∈ files ⊦ content0[n0] = (content0 ⊕ mkcontent(ino0, pcache))[n0], datakey(ino0, n0) = datakey(ino, n), datakey(ino, n) ∈ pcache, datakey(ino0, n0) ∈ pcache

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] → [n0, mkcontent(ino0, pcache), content0] flags: <all paths>

Additional information

Used simplifier rules: at-overwrite-content-old: ⊦ ¬ n ∈ content1 → (content0 ⊕ content1)[n] = content0[n];%at-mkcontent: ⊦ mkcontent(ino, pcache)[n] = pcache[datakey(ino, n)].page;%in-mkcontent: ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache;% ⊦ ¬ key ∈ pcache → pcache[key] = (∅)[key]; (s) Used terms: n0, mkcontent(ino0, pcache), content0