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Proof step 787 from proof overwrite-write-page-clean (previous step)

files[ino0] = mkfile(m4, md1, m5, content1), ((files ⊕ pcache) ⊕ icache)[ino] = mkfile(m0, md, m1, content), files[ino] = mkfile(m2, md0, m3, content0), datakey(ino, n) ∈ pcache, n ∈ content0, ino ∈ files, ino0 ∈ files, ino ∈ icache, datakey(ino, n) ∈ pcache[datakey(ino, m), mkpentry(false, buf)] ⊦ content1[n] = (content1 ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)]))[n], n = m, ino0 ∈ icache, datakey(ino0, n) ∈ pcache

Heuristic weak cut applied rule cut formula

And closed the goal!

Rule argument

fma: n ∈ 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;%at-overwrite-content-old: ⊦ ¬ n ∈ content1 → (content0 ⊕ content1)[n] = content0[n];% ⊦ key ∈ pcache[key0, pe] ↔ key = key0 ∨ key ∈ pcache; (ws)% ⊦ datakey(m, m0) = datakey(m1, m2) ↔ m = m1 ∧ m0 = m2; (ws) Used formulas: n ∈ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)])