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Proof step 540 from proof fsync-pages-keep-abs (previous step)

# buf = VFS_PAGE_SIZE, files0[m] = mkfile(m9, md2, m10, content), files1[m] = mkfile(m9, md2, m10, content1), icache[m] = mkientry(boolvar0, mkinode(m3, md0, true, m4, m5, m6)), pcache[datakey(m, n)] = mkpentry(true, buf), content ⊕ mkcontent(m, pcache) = content1 ⊕ mkcontent(m, pcache0), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), m ∈ icache, datakey(m, n) ∈ pcache, m ∈ files1, m ∈ files0, ⌊err0⌋ ⊦ content1 ⊕ mkcontent(m, pcache0) = content[n, buf] ⊕ mkcontent(m, pcache)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 541:
⊦ content = content0 ↔ (∀ n. (n ∈ content ↔ n ∈ content0) ∧ (n ∈ content → content[n] = content0[n]))
Proof step 542:
# buf = VFS_PAGE_SIZE, pcache[datakey(m, n)] = mkpentry(true, buf), icache[m] = mkientry(boolvar0, mkinode(m3, md0, true, m4, m5, m6)), files1[m] = mkfile(m9, md2, m10, content1), files0[m] = mkfile(m9, md2, m10, content), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), m ∈ files0, m ∈ files1, datakey(m, n) ∈ pcache, m ∈ icache, ⌊err0⌋ , ∀ n. (n ∈ content ⊕ mkcontent(m, pcache) ↔ n ∈ content1 ⊕ mkcontent(m, pcache0)) ∧ (n ∈ content ⊕ mkcontent(m, pcache) → (content ⊕ mkcontent(m, pcache))[n] = (content1 ⊕ mkcontent(m, pcache0))[n]) ⊦ content1 ⊕ mkcontent(m, pcache0) = content[n, buf] ⊕ mkcontent(m, pcache)

Rule argument

spec: store, inst: file-content name: k-Extension seq: ⊦ content = content0 ↔ (∀ n. (n ∈ content ↔ n ∈ content0) ∧ (n ∈ content → content[n] = content0[n])) subst: [content0, content] → [content1 ⊕ mkcontent(m, pcache0), content ⊕ mkcontent(m, pcache)] flags: <all paths>

Additional information

Used terms: content1 ⊕ mkcontent(m, pcache0), content ⊕ mkcontent(m, pcache)