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Proof step 16 from proof at-pcache-overwrite-other (previous step)

files[ino] = mkfile(m, md, m0, content), n ∈ content ⊕ mkcontent(ino, pcache[key0, pe]), n ∈ content ⊕ mkcontent(ino, pcache) ⊦ (content ⊕ mkcontent(ino, pcache[key0, pe]))[n] = (content ⊕ mkcontent(ino, pcache))[n], ino = key0.ino, n ∈ mkcontent(ino, pcache[key0, pe])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
files[ino] = mkfile(m, md, m0, content), n ∈ content ⊕ mkcontent(ino, pcache), n ∈ content ⊦ content[n] = (content ⊕ mkcontent(ino, pcache))[n], datakey(ino, n) = key0, ino = key0.ino, datakey(ino, n) ∈ pcache

Rule argument

Additional information

Used simplifier rules: ⊦ key ∈ pcache[key0, pe] ↔ key = key0 ∨ key ∈ pcache; (ws)% ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache; (s)% ⊦ n ∈ content0 ⊕ content1 ↔ n ∈ content0 ∨ n ∈ content1; (ws)% ⊦ ¬ n ∈ content1 → (content0 ⊕ content1)[n] = content0[n]; (s)