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Proof step 214 from proof overwrite-write-page-clean (previous step)

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 215:
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), ino ∈ icache, ino0 ∈ files, ino ∈ files, ino0 ∈ icache ⊦ (content1 ⊕ mkcontent(ino0, pcache))[m] = (content1 ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)]))[m], datakey(ino0, m) = datakey(ino, m), datakey(ino0, m) ∈ pcache, m ∈ content1, m ∈ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)])

Rule argument

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

Additional information

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