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Proof step 851 from proof overwrite-write-page-clean (previous step)

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

And obtained the following new goals

Proof step 852:
files[ino] = mkfile(m2, md0, m3, content0), ino ∈ files ⊦ buf = (content0[m, buf] ⊕ mkcontent(ino, pcache[datakey(ino, m), mkpentry(false, buf)]))[m], ino ∈ icache

Rule argument

Additional information

Used simplifier rules: in-overwrite-content: ⊦ n ∈ content0 ⊕ content1 ↔ n ∈ content0 ∨ n ∈ content1;%in-overwrite-content: ⊦ n ∈ content0 ⊕ content1 ↔ n ∈ content0 ∨ n ∈ content1;% ⊦ content[n, buf][n] = buf; (s)% ⊦ n ∈ content[n, buf]; (s)% ⊦ key ∈ pcache[key, pe]; (s)