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Proof step 135 from proof overwrite-write-page-dirty (previous step)

((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), ino0 ∈ icache, ino ∈ files, ino0 ∈ files ⊦ (ino0 = ino ⊃ mkfile(m0, md, m1, content[m, buf]);((files ⊕ pcache) ⊕ icache)[ino0]) = ((files ⊕ pcache[datakey(ino, m), mkpentry(true, buf)]) ⊕ icache)[ino0], ino ∈ icache

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 136:
ino0 ∈ icache, ino ∈ files, ino0 ∈ files ⊦ ((files ⊕ pcache) ⊕ icache)[ino0] = ((files ⊕ pcache[datakey(ino, m), mkpentry(true, buf)]) ⊕ icache)[ino0], ino ∈ icache

Rule argument

Additional information

Used simplifier rules: at-icache-overwrite-not-cached: ⊦ ¬ ino ∈ icache → (files ⊕ icache)[ino] = files[ino];%at-pcache-overwrite: ⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache));%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)