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Proof step 14 from proof at-pcache-overwrite-other (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ n ∈ content1 → (content0 ⊕ content1)[n] = content1[n]
Proof step 16:
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])
Proof step 19:
files[ino] = mkfile(m, md, m0, content), n ∈ content ⊕ mkcontent(ino, pcache[key0, pe]), n ∈ content ⊕ mkcontent(ino, pcache), n ∈ mkcontent(ino, pcache[key0, pe]) ⊦ mkcontent(ino, pcache[key0, pe])[n] = (content ⊕ mkcontent(ino, pcache))[n], ino = key0.ino

Rule argument

spec: cache-base name: at-overwrite-content-new seq: ⊦ n ∈ content1 → (content0 ⊕ content1)[n] = content1[n] subst: [n, content1, content0] → [n, mkcontent(ino, pcache[key0, pe]), content] flags: <all paths>

Additional information

Used terms: n, mkcontent(ino, pcache[key0, pe]), content