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Proof step 45 from proof overwrite-write-page-clean (previous step)

icache[ino] = mkientry(boolvar, mkinode(m0, md, true, m1, m4, m5)), files[ino] = mkfile(m2, md0, m3, content0), ino ∈ icache, ino ∈ files, datakey(ino, n) ∈ pcache[datakey(ino, m), mkpentry(false, buf)] ⊦ n = m, n ∈ content0, (n ∈ content0 ⊕ mkcontent(ino, pcache) ↔ n ∈ content0[m, buf] ⊕ mkcontent(ino, pcache[datakey(ino, m), mkpentry(false, buf)])) ∧ (content0 ⊕ mkcontent(ino, pcache))[n] = (content0[m, buf] ⊕ mkcontent(ino, pcache[datakey(ino, m), mkpentry(false, buf)]))[n]

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 46:
files[ino] = mkfile(m2, md0, m3, content0), icache[ino] = mkientry(boolvar, mkinode(m0, md, true, m1, m4, m5)), datakey(ino, n) ∈ pcache[datakey(ino, m), mkpentry(false, buf)], ino ∈ files, ino ∈ icache, n ∈ mkcontent(ino, pcache) ⊦ n = m, n ∈ content0, (n ∈ content0 ⊕ mkcontent(ino, pcache) ↔ n ∈ content0[m, buf] ⊕ mkcontent(ino, pcache[datakey(ino, m), mkpentry(false, buf)])) ∧ (content0 ⊕ mkcontent(ino, pcache))[n] = (content0[m, buf] ⊕ mkcontent(ino, pcache[datakey(ino, m), mkpentry(false, buf)]))[n]

Rule argument

fma: n ∈ mkcontent(ino, pcache)

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: n ∈ mkcontent(ino, pcache)