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Proof step 206 from proof overwrite-write-page-dirty (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 207:
files[ino0] = mkfile(m2, md0, m3, content0), ((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), ino ∈ files, ino0 ∈ files, ino ∈ icache ⊦ n ∈ content0 ⊕ mkcontent(ino0, pcache) ↔ n ∈ content0 ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(true, buf)]), ino0 ∈ icache
Proof step 212:
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

Rule argument

pos: right 2

Proof step 206 from proof overwrite-write-page-dirty (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information