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Proof step 212 from proof overwrite-write-page-dirty (previous step)

files[ino0] = mkfile(m2, md0, m3, content0), ((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), ino ∈ files, ino0 ∈ files, ino ∈ icache ⊦ (content0 ⊕ mkcontent(ino0, pcache))[n] = (content0 ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(true, buf)]))[n], ino0 ∈ icache

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 213:
⊦ n ∈ content1 → (content0 ⊕ content1)[n] = content1[n]
Proof step 214:
((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), files[ino0] = mkfile(m2, md0, m3, content0), ino ∈ icache, ino0 ∈ files, ino ∈ files ⊦ (content0 ⊕ mkcontent(ino0, pcache))[n] = (content0 ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(true, buf)]))[n], ino0 ∈ icache, n ∈ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(true, buf)])
Proof step 217:
((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), files[ino0] = mkfile(m2, md0, m3, content0), ino ∈ icache, ino0 ∈ files, ino ∈ files, n ∈ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(true, buf)]) ⊦ (content0 ⊕ mkcontent(ino0, pcache))[n] = mkcontent(ino0, pcache[datakey(ino, m), mkpentry(true, buf)])[n], ino0 ∈ icache

Rule argument

spec: <toplevel> name: at-overwrite-content-new seq: ⊦ n ∈ content1 → (content0 ⊕ content1)[n] = content1[n] subst: [n, content1, content0] → [n, mkcontent (ino0, pcache[datakey(ino, m), mkpentry(true, buf)]), content0] flags: <all paths>

Additional information

Used terms: n, mkcontent(ino0, pcache[datakey(ino, m), mkpentry(true, buf)]), content0