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Proof step 90 from proof fsync-pages-others-unchanged (previous step)

# buf0 = VFS_PAGE_SIZE, (content0 ⊕ mkcontent(ino0, pcache))[n0] = (content1 ⊕ mkcontent(ino0, pcache0))[n0], 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), pcache[datakey(m, n), mkpentry(false, buf0)][datakey(ino0, n0)] = mkpentry(boolvar, buf), n * VFS_PAGE_SIZE < m2, datakey(ino0, n0) ∈ pcache[datakey(m, n), mkpentry(false, buf0)], n0 ∈ content1 ⊕ mkcontent(ino0, pcache0), n0 ∈ content0 ⊕ mkcontent(ino0, pcache), ino0 ∈ files1, ino0 ∈ files0, datakey(m, n) ∈ pcache, m ∈ files1, n0 ∈ content0 ⊕ mkcontent(ino0, pcache[datakey(m, n), mkpentry(false, buf0)]), ∀ 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]) ⊦ buf = (content1 ⊕ mkcontent(ino0, pcache0))[n0], ino0 = m

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 91:
⊦ key ≠ key0 → pcache[key0, pe][key] = pcache[key]
Proof step 92:
# buf0 = VFS_PAGE_SIZE, pcache[datakey(ino0, n0)] = mkpentry(boolvar, buf), 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))[n0] = (content1 ⊕ mkcontent(ino0, pcache0))[n0], n * VFS_PAGE_SIZE < m2, n0 ∈ content0 ⊕ mkcontent(ino0, pcache[datakey(m, n), mkpentry(false, buf0)]), m ∈ files1, datakey(m, n) ∈ pcache, ino0 ∈ files0, ino0 ∈ files1, n0 ∈ content0 ⊕ mkcontent(ino0, pcache), n0 ∈ content1 ⊕ mkcontent(ino0, pcache0), datakey(ino0, n0) ∈ pcache[datakey(m, n), mkpentry(false, buf0)], ∀ 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]), ∀ 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 ⊦ buf = (content1 ⊕ mkcontent(ino0, pcache0))[n0], datakey(ino0, n0) = datakey(m, n), ino0 = m

Rule argument

spec: store, inst: pcache name: At-other seq: ⊦ key ≠ key0 → pcache[key0, pe][key] = pcache[key] subst: [key, pe, key0, pcache] → [datakey(ino0, n0), mkpentry(false, buf0), datakey(m, n), pcache] flags: List([[0,0,6,1,0]])

Additional information

Used simplifier rules: ⊦ datakey(m, m0) = datakey(m1, m2) ↔ m = m1 ∧ m0 = m2; (ws) Used terms: datakey(ino0, n0), mkpentry(false, buf0), datakey(m, n), pcache