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Proof step 911 from proof overwrite-write-page-clean (previous step)

files[ino0] = mkfile(m4, md1, m5, content1), files[ino] = mkfile(m2, md0, m3, content0), ino0 ∈ files, ino ∈ files ⊦ ino0 = ino, content1 ⊕ mkcontent(ino0, pcache) = content1 ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)]), ino ∈ icache, ino0 ∈ icache

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 912:
⊦ content = content0 ↔ (∀ n. (n ∈ content ↔ n ∈ content0) ∧ content[n] = content0[n])
Proof step 913:
files[ino] = mkfile(m2, md0, m3, content0), files[ino0] = mkfile(m4, md1, m5, content1), ino ∈ files, ino0 ∈ files ⊦ ino0 = ino, ino0 ∈ icache, ino ∈ icache, ∀ n. (n ∈ content1 ⊕ mkcontent(ino0, pcache) ↔ n ∈ content1 ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)])) ∧ (content1 ⊕ mkcontent(ino0, pcache))[n] = (content1 ⊕ mkcontent(ino0, 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] → [ content1 ⊕ mkcontent (ino0, pcache[datakey(ino, m), mkpentry(false, buf)]), content1 ⊕ mkcontent(ino0, pcache)] flags: <all paths>

Additional information

Used terms: content1 ⊕ mkcontent(ino0, pcache[datakey(ino, m), mkpentry(false, buf)]), content1 ⊕ mkcontent(ino0, pcache)