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Proof step 69 from proof fsync-pages-others-unchanged (previous step)

# buf0 = VFS_PAGE_SIZE, files1[ino0] = mkfile(m5, md1, m6, content0), files1[m] = mkfile(m0, md, m1, content), pcache[datakey(m, n)] = mkpentry(true, buf0), files0[ino0] = mkfile(m5, md1, m6, content1), content0 ⊕ mkcontent(ino0, pcache) = content1 ⊕ mkcontent(ino0, pcache0), n * VFS_PAGE_SIZE < m2, m ∈ files1, datakey(m, n) ∈ pcache, ino0 ∈ files0, ino0 ∈ files1, ∀ ino. ino ≠ m ∧ ino ∈ files0 → mkfile(files1[ino].size, files1[ino].meta, files1[ino].nlink, files1[ino].content ⊕ mkcontent(ino, pcache)) = mkfile(files0[ino].size, files0[ino].meta, files0[ino].nlink, files0[ino].content ⊕ mkcontent(ino, pcache0)) ∧ ino ∈ files1 ⊦ ino0 = m, (n0 ∈ content0 ⊕ mkcontent(ino0, pcache[datakey(m, n), mkpentry(false, buf0)]) ↔ n0 ∈ content1 ⊕ mkcontent(ino0, pcache0)) ∧ ( n0 ∈ content0 ⊕ mkcontent(ino0, pcache[datakey(m, n), mkpentry(false, buf0)]) → (content0 ⊕ mkcontent(ino0, pcache[datakey(m, n), mkpentry(false, buf0)]))[n0] = (content1 ⊕ mkcontent(ino0, pcache0))[n0])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 70:
⊦ content = content0 ↔ (∀ n. (n ∈ content ↔ n ∈ content0) ∧ (n ∈ content → content[n] = content0[n]))
Proof step 71:
# buf0 = VFS_PAGE_SIZE, files0[ino0] = mkfile(m5, md1, m6, content1), pcache[datakey(m, n)] = mkpentry(true, buf0), files1[m] = mkfile(m0, md, m1, content), files1[ino0] = mkfile(m5, md1, m6, content0), n * VFS_PAGE_SIZE < m2, ino0 ∈ files1, ino0 ∈ files0, datakey(m, n) ∈ pcache, m ∈ files1, ∀ ino. ino ≠ m ∧ ino ∈ files0 → mkfile(files1[ino].size, files1[ino].meta, files1[ino].nlink, files1[ino].content ⊕ mkcontent(ino, pcache)) = mkfile(files0[ino].size, files0[ino].meta, files0[ino].nlink, files0[ino].content ⊕ mkcontent(ino, pcache0)) ∧ ino ∈ files1, ∀ n. (n ∈ content0 ⊕ mkcontent(ino0, pcache) ↔ n ∈ content1 ⊕ mkcontent(ino0, pcache0)) ∧ (n ∈ content0 ⊕ mkcontent(ino0, pcache) → (content0 ⊕ mkcontent(ino0, pcache))[n] = (content1 ⊕ mkcontent(ino0, pcache0))[n]) ⊦ ino0 = m, (n0 ∈ content0 ⊕ mkcontent(ino0, pcache[datakey(m, n), mkpentry(false, buf0)]) ↔ n0 ∈ content1 ⊕ mkcontent(ino0, pcache0)) ∧ ( n0 ∈ content0 ⊕ mkcontent(ino0, pcache[datakey(m, n), mkpentry(false, buf0)]) → (content0 ⊕ mkcontent(ino0, pcache[datakey(m, n), mkpentry(false, buf0)]))[n0] = (content1 ⊕ mkcontent(ino0, pcache0))[n0])

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(ino0, pcache0), content0 ⊕ mkcontent(ino0, pcache)] flags: List([[0,0,5]])

Additional information

Used terms: content1 ⊕ mkcontent(ino0, pcache0), content0 ⊕ mkcontent(ino0, pcache)