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Proof step 11 from proof at-pcache-overwrite-other (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
files[ino] = mkfile(m, md, m0, content), n ∈ content ⊕ mkcontent(ino, pcache[key0, pe]) ⊦ ino = key0.ino, n ∈ content ⊕ mkcontent(ino, pcache) ∧ (content ⊕ mkcontent(ino, pcache[key0, pe]))[n] = (content ⊕ mkcontent(ino, pcache))[n]

Proof step 11 from proof at-pcache-overwrite-other (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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