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Proof step 844 from proof overwrite-write-page-clean (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 845:
⊦ content = content0 ↔ (∀ n. (n ∈ content ↔ n ∈ content0) ∧ content[n] = content0[n])
Proof step 846:
files[ino] = mkfile(m2, md0, m3, content0), ino ∈ files ⊦ ino ∈ icache, ∀ n. (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]

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[m, buf] ⊕ mkcontent (ino, pcache[datakey(ino, m), mkpentry(false, buf)]), (content0 ⊕ mkcontent(ino, pcache))[m, buf]] flags: <all paths>

Additional information

Used terms: content0[m, buf] ⊕ mkcontent(ino, pcache[datakey(ino, m), mkpentry(false, buf)]), (content0 ⊕ mkcontent(ino, pcache))[m, buf]