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Proof step 10 from proof overwrite-write-page-clean (previous step)

files[ino] = mkfile(m2, md0, m3, content0), ((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), ino0 ∈ files, ino ∈ files, ino0 ∈ icache ⊦ (ino0 = ino ⊃ mkfile(m0, md, m1, content[m, buf]);((files ⊕ pcache) ⊕ icache)[ino0]) = ((files[ino, mkfile(m2, md0, m3, content0[m, buf])] ⊕ pcache[datakey(ino, m), mkpentry(false, buf)]) ⊕ icache)[ino0]

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 11:
((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), files[ino] = mkfile(m2, md0, m3, content0), ino0 ∈ icache, ino ∈ files, ino0 ∈ files, ino ∈ icache ⊦ (ino0 = ino ⊃ mkfile(m0, md, m1, content[m, buf]);((files ⊕ pcache) ⊕ icache)[ino0]) = ((files[ino, mkfile(m2, md0, m3, content0[m, buf])] ⊕ pcache[datakey(ino, m), mkpentry(false, buf)]) ⊕ icache)[ino0]
Proof step 430:
((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), files[ino] = mkfile(m2, md0, m3, content0), ino0 ∈ icache, ino ∈ files, ino0 ∈ files ⊦ (ino0 = ino ⊃ mkfile(m0, md, m1, content[m, buf]);((files ⊕ pcache) ⊕ icache)[ino0]) = ((files[ino, mkfile(m2, md0, m3, content0[m, buf])] ⊕ pcache[datakey(ino, m), mkpentry(false, buf)]) ⊕ icache)[ino0], ino ∈ icache

Rule argument

fma: ino ∈ icache

Additional information

Used formulas: ino ∈ icache