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Proof step 121 from proof overwrite-write-page-clean (previous step)

pcache[datakey(ino, m), mkpentry(false, buf)][datakey(ino, n)] = mkpentry(boolvar0, buf0), files[ino] = mkfile(m2, md0, m3, content0), icache[ino] = mkientry(boolvar, mkinode(m0, md, false, m1, m4, m5)), datakey(ino, n) ∈ pcache, ino ∈ icache, ino ∈ files, datakey(ino, n) ∈ pcache[datakey(ino, m), mkpentry(false, buf)] ⊦ (content0 ⊕ mkcontent(ino, pcache))[n] = buf0, datakey(ino, n) = datakey(ino, m), n = m, n ∈ content0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 122:
icache[ino] = mkientry(boolvar, mkinode(m0, md, false, m1, m4, m5)), files[ino] = mkfile(m2, md0, m3, content0), pcache[datakey(ino, n)] = mkpentry(boolvar0, buf0), ino ∈ files, ino ∈ icache, datakey(ino, n) ∈ pcache ⊦ (content0 ⊕ mkcontent(ino, pcache))[n] = buf0, datakey(ino, n) = datakey(ino, m), n ∈ content0

Rule argument

Additional information

Used simplifier rules: ⊦ key ≠ key0 → (key ∈ pcache[key0, pe] ↔ key ∈ pcache); (s)% ⊦ key ≠ key0 → pcache[key0, pe][key] = pcache[key]; (s)