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Proof step 510 from proof overwrite-write-page-clean (previous step)

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)] ⊦ n ∈ content ⊕ mkcontent(ino0, pcache) ↔ n ∈ content ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)]), n = m, ino ∈ icache, datakey(ino0, m) ∈ pcache

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 511:
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), datakey(ino, n) ∈ pcache[datakey(ino, m), mkpentry(false, buf)], ino0 ∈ icache, ino ∈ files, ino0 ∈ files, n ∈ content0, datakey(ino, n) ∈ pcache ⊦ n ∈ content ⊕ mkcontent(ino0, pcache) ↔ n ∈ content ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)]), n = m, datakey(ino0, m) ∈ pcache, ino ∈ icache, 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: in-mkcontent: ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache;% ⊦ key ∈ pcache[key0, pe] ↔ key = key0 ∨ key ∈ pcache; (ws)% ⊦ datakey(m, m0) = datakey(m1, m2) ↔ m = m1 ∧ m0 = m2; (ws) Used formulas: m ∈ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)])