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Proof step 10 from proof pcache-overwrite-read-page (previous step)

files[ino] = mkfile(m, md, m0, content), files[ino0] = mkfile(m1, md0, m2, content0), ino0 ∈ files, ino ∈ files, n ∈ content ⊦ content0 ⊕ mkcontent(ino0, pcache[datakey(ino, n), mkpentry(false, content[n])]) = content0 ⊕ mkcontent(ino0, pcache), datakey(ino, n) ∈ pcache

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ content = content0 ↔ (∀ n. (n ∈ content ↔ n ∈ content0) ∧ content[n] = content0[n])
Proof step 12:
files[ino0] = mkfile(m1, md0, m2, content0), files[ino] = mkfile(m, md, m0, content), n ∈ content, ino ∈ files, ino0 ∈ files ⊦ datakey(ino, n) ∈ pcache, ∀ n0. (n0 ∈ content0 ⊕ mkcontent(ino0, pcache[datakey(ino, n), mkpentry(false, content[n])]) ↔ n0 ∈ content0 ⊕ mkcontent(ino0, pcache)) ∧ (content0 ⊕ mkcontent(ino0, pcache[datakey(ino, n), mkpentry(false, content[n])]))[n0] = (content0 ⊕ mkcontent(ino0, pcache))[n0]

Rule argument

spec: store, inst: file-content name: Extension seq: ⊦ content = content0 ↔ (∀ n. (n ∈ content ↔ n ∈ content0) ∧ content[n] = content0[n]) subst: [content0, content] → [content0 ⊕ mkcontent(ino0, pcache), content0 ⊕ mkcontent (ino0, pcache[datakey(ino, n), mkpentry(false, content[n])])] flags: <all paths>

Additional information

Used terms: content0 ⊕ mkcontent(ino0, pcache), content0 ⊕ mkcontent (ino0, pcache[datakey(ino, n), mkpentry(false, content[n])])