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Proof step 64 from proof overwrite-write-page-dirty (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 65:
⊦ n ∈ content1 → (content0 ⊕ content1)[n] = content1[n]
Proof step 66:
icache[ino] = mkientry(boolvar, mkinode(m0, md, false, m1, m2, m3)), files[ino] = mkfile(m4, md0, m5, content), ino ∈ icache, ino ∈ files ⊦ (content ⊕ mkcontent(ino, pcache))[n] = (content ⊕ mkcontent(ino, pcache[datakey(ino, m), mkpentry(true, buf)]))[n], n = m, n ∈ mkcontent(ino, pcache[datakey(ino, m), mkpentry(true, buf)])
Proof step 69:
icache[ino] = mkientry(boolvar, mkinode(m0, md, false, m1, m2, m3)), files[ino] = mkfile(m4, md0, m5, content), ino ∈ icache, ino ∈ files, n ∈ mkcontent(ino, pcache[datakey(ino, m), mkpentry(true, buf)]) ⊦ (content ⊕ mkcontent(ino, pcache))[n] = mkcontent(ino, pcache[datakey(ino, m), mkpentry(true, buf)])[n], n = m

Rule argument

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

Additional information

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