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Proof step 53 from proof overwrite-write-page-dirty (previous step)

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 54:
files[ino] = mkfile(m4, md0, m5, content), icache[ino] = mkientry(boolvar, mkinode(m0, md, false, m1, m2, m3)), n = m, ino ∈ files, ino ∈ icache ⊦ (n ∈ (content ⊕ mkcontent(ino, pcache))[m, buf] ↔ n ∈ content ⊕ mkcontent(ino, pcache[datakey(ino, m), mkpentry(true, buf)])) ∧ (content ⊕ mkcontent(ino, pcache))[m, buf][n] = (content ⊕ mkcontent(ino, pcache[datakey(ino, m), mkpentry(true, buf)]))[n]
Proof step 57:
files[ino] = mkfile(m4, md0, m5, content), icache[ino] = mkientry(boolvar, mkinode(m0, md, false, m1, m2, m3)), ino ∈ files, ino ∈ icache ⊦ n = m, (n ∈ (content ⊕ mkcontent(ino, pcache))[m, buf] ↔ n ∈ content ⊕ mkcontent(ino, pcache[datakey(ino, m), mkpentry(true, buf)])) ∧ (content ⊕ mkcontent(ino, pcache))[m, buf][n] = (content ⊕ mkcontent(ino, pcache[datakey(ino, m), mkpentry(true, buf)]))[n]

Rule argument

fma: n = m

Additional information

Used formulas: n = m