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Proof step 127 from proof overwrite-write-page-clean (previous step)

icache[ino] = mkientry(boolvar, mkinode(m0, md, false, m1, m4, m5)), files[ino] = mkfile(m2, md0, m3, content0), ino ∈ files, ino ∈ icache ⊦ datakey(ino, n) = datakey(ino, m), datakey(ino, n) ∈ pcache, (n ∈ (content0 ⊕ mkcontent(ino, pcache))[m, buf] ↔ n ∈ content0[m, buf] ⊕ mkcontent(ino, pcache[datakey(ino, m), mkpentry(false, buf)])) ∧ (content0 ⊕ mkcontent(ino, pcache))[m, buf][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 128:
files[ino] = mkfile(m2, md0, m3, content0), icache[ino] = mkientry(boolvar, mkinode(m0, md, false, m1, m4, m5)), ino ∈ icache, ino ∈ files, n ∈ content0[m, buf] ⊦ datakey(ino, n) = datakey(ino, m), datakey(ino, n) ∈ pcache, (n ∈ (content0 ⊕ mkcontent(ino, pcache))[m, buf] ↔ n ∈ content0[m, buf] ⊕ mkcontent(ino, pcache[datakey(ino, m), mkpentry(false, buf)])) ∧ (content0 ⊕ mkcontent(ino, pcache))[m, buf][n] = (content0[m, buf] ⊕ mkcontent(ino, pcache[datakey(ino, m), mkpentry(false, buf)]))[n]
Proof step 139:
files[ino] = mkfile(m2, md0, m3, content0), icache[ino] = mkientry(boolvar, mkinode(m0, md, false, m1, m4, m5)), ino ∈ icache, ino ∈ files ⊦ datakey(ino, n) = datakey(ino, m), datakey(ino, n) ∈ pcache, n ∈ content0[m, buf], (n ∈ (content0 ⊕ mkcontent(ino, pcache))[m, buf] ↔ n ∈ content0[m, buf] ⊕ mkcontent(ino, pcache[datakey(ino, m), mkpentry(false, buf)])) ∧ (content0 ⊕ mkcontent(ino, pcache))[m, buf][n] = (content0[m, buf] ⊕ mkcontent(ino, pcache[datakey(ino, m), mkpentry(false, buf)]))[n]

Rule argument

fma: n ∈ content0[m, buf]

Additional information

Used formulas: n ∈ content0[m, buf]