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Proof step 868 from proof overwrite-write-page-clean (previous step)

files[ino] = mkfile(m2, md0, m3, content0), ino ∈ files, datakey(ino, n) ∈ pcache[datakey(ino, m), mkpentry(false, buf)], datakey(ino, n) ∈ pcache ⊦ n = m, ino ∈ icache, 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]

User applied rule case distinction

And obtained the following new goals

Proof step 869:
files[ino] = mkfile(m2, md0, m3, content0), datakey(ino, n) ∈ pcache, datakey(ino, n) ∈ pcache[datakey(ino, m), mkpentry(false, buf)], ino ∈ files ⊦ (content0 ⊕ mkcontent(ino, pcache))[n] = (content0[m, buf] ⊕ mkcontent(ino, pcache[datakey(ino, m), mkpentry(false, buf)]))[n], n = m, n ∈ content0, ino ∈ icache

Rule argument

pos: right 4

Additional information

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