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Proof step 368 from proof overwrite-write-page-clean (previous step)

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 369:
pcache[datakey(ino0, n)] = mkpentry(boolvar0, buf0), ((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), files[ino] = mkfile(m2, md0, m3, content0), icache[ino0] = mkientry(boolvar, mkinode(m4, md1, false, m5, m6, m7)), files[ino0] = mkfile(m8, md2, m9, content1), datakey(ino, n) ∈ pcache, n ∈ content0, ino ∈ files, ino0 ∈ files, ino ∈ icache, ino0 ∈ icache, datakey(ino, n) ∈ pcache[datakey(ino, m), mkpentry(false, buf)], datakey(ino0, n) ∈ pcache, n ∈ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)]) ⊦ buf0 = (content1 ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)]))[n], ino0 = ino, n = m

Rule argument

fma: n ∈ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)])

Additional information

Used simplifier rules: at-overwrite-content-old: ⊦ ¬ n ∈ content1 → (content0 ⊕ content1)[n] = content0[n];%in-mkcontent: ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache;% ⊦ key ∈ pcache[key0, pe] ↔ key = key0 ∨ key ∈ pcache; (ws) Used formulas: n ∈ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)])