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Proof step 520 from proof overwrite-write-page-clean (previous step)

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 521:
pcache[datakey(ino0, n)] = mkpentry(boolvar0, buf0), files[ino] = mkfile(m2, md0, m3, content0), icache[ino0] = mkientry(boolvar, mkinode(m0, md, true, m1, m4, m5)), files[ino0] = mkfile(m6, md1, m7, content), datakey(ino, n) ∈ pcache, n ∈ content0, ino0 ∈ files, ino ∈ files, 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 = (content ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)]))[n], n = m, ino ∈ icache

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)])