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Proof step 7 from proof overwrite-write-page-dirty (previous step)

((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), 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]

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 8:
((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 ⊕ pcache[datakey(ino, m), mkpentry(true, buf)]) ⊕ icache)[ino0]
Proof step 196:
((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), ino0 ∈ files, ino ∈ files ⊦ (ino0 = ino ⊃ mkfile(m0, md, m1, content[m, buf]);((files ⊕ pcache) ⊕ icache)[ino0]) = ((files ⊕ pcache[datakey(ino, m), mkpentry(true, buf)]) ⊕ icache)[ino0], ino0 ∈ icache

Rule argument

fma: ino0 ∈ icache

Additional information

Used formulas: ino0 ∈ icache