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Proof step 473 from proof overwrite-write-page-clean (previous step)

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

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] → [m, mkcontent(ino0, 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;% ⊦ ¬ key ∈ pcache → pcache[key] = (∅)[key]; (s) Used terms: m, mkcontent(ino0, pcache), content