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Proof step 253 from proof overwrite-write-page-clean (previous step)

pcache[datakey(ino0, n)] = mkpentry(boolvar0, buf0), files[ino0] = mkfile(m8, md2, m9, content1), icache[ino0] = mkientry(boolvar, mkinode(m4, md1, true, m5, m6, m7)), files[ino] = mkfile(m2, md0, m3, content0), ((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), pcache[datakey(ino, m), mkpentry(false, buf)][datakey(ino0, n)] = mkpentry(boolvar1, buf1), datakey(ino0, n) ∈ pcache[datakey(ino, m), mkpentry(false, buf)], datakey(ino, n) ∈ pcache, datakey(ino, n) ∈ pcache[datakey(ino, m), mkpentry(false, buf)], ino ∈ icache, ino0 ∈ files, ino ∈ files, ino0 ∈ icache, datakey(ino0, n) ∈ pcache ⊦ buf0 = buf1, ino0 = ino, n = m, n ∈ content0

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: datakey(ino0, n) = datakey(ino, m)

Additional information

Used simplifier rules: ⊦ key ≠ key0 → pcache[key0, pe][key] = pcache[key]; (s)% ⊦ key ≠ key0 → (key ∈ pcache[key0, pe] ↔ key ∈ pcache); (s)%⊦ mkpentry(boolvar, buf) = mkpentry(boolvar0, buf0) ↔ (boolvar ↔ boolvar0) ∧ buf = buf0; (ws)% ⊦ datakey(m, m0) = datakey(m1, m2) ↔ m = m1 ∧ m0 = m2; (ws) Used formulas: datakey(ino0, n) = datakey(ino, m)