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Proof step 60 from proof overwrite-write-page-clean (previous step)

files[ino] = mkfile(m2, md0, m3, content0), icache[ino] = mkientry(boolvar, mkinode(m0, md, true, m1, m4, m5)), ino ∈ files, ino ∈ icache, 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]

User applied rule case distinction

And obtained the following new goals

Proof step 61:
icache[ino] = mkientry(boolvar, mkinode(m0, md, true, m1, m4, m5)), files[ino] = mkfile(m2, md0, m3, content0), n ∈ content0[m, buf], ino ∈ icache, ino ∈ files ⊦ (content0 ⊕ mkcontent(ino, pcache))[m, buf][n] = (content0[m, buf] ⊕ mkcontent(ino, pcache[datakey(ino, m), mkpentry(false, buf)]))[n], datakey(ino, n) = datakey(ino, m), datakey(ino, n) ∈ pcache

Rule argument

pos: right 3

Additional information

Used simplifier rules: in-overwrite-content: ⊦ n ∈ content0 ⊕ content1 ↔ n ∈ content0 ∨ n ∈ content1;% ⊦ n ∈ content[n0, buf] ↔ n = n0 ∨ n ∈ content; (ws)% ⊦ n ≠ n0 → (n ∈ content[n0, buf] ↔ n ∈ content); (s)