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Proof step 193 from proof fsync-pages-keep-abs (previous step)

# buf = VFS_PAGE_SIZE, pcache[datakey(m, n)] = mkpentry(true, buf), (∅)[m] = mkientry(boolvar0, mkinode(m3, md0, boolvar, m4, m5, m6)), content[n0] = content1[n0], files1[m] = mkfile(m9, md2, m10, content1), files0[m] = mkfile(m9, md2, m10, content), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), n0 ∈ content, n0 ∈ content1 ⊕ mkcontent(m, pcache0), m ∈ files0, m ∈ files1, datakey(m, n) ∈ pcache, n0 ∈ content1, ∀ ino0. (ino0 ∈ files0 ↔ ino0 ∈ files1) ∧ (ino0 ∈ files0 → ((files0 ⊕ pcache) ⊕ icache)[ino0] = ((files1 ⊕ pcache0) ⊕ icache)[ino0]) ⊦ (content1 ⊕ mkcontent(m, pcache0))[n0] = content[n, buf][n0], datakey(m, n0) = datakey(m, n), datakey(m, n0) ∈ pcache0, m ∈ icache, datakey(m, n0) ∈ pcache

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 194:
⊦ n ∈ content1 → (content0 ⊕ content1)[n] = content1[n]
Proof step 195:
# buf = VFS_PAGE_SIZE, files0[m] = mkfile(m9, md2, m10, content), files1[m] = mkfile(m9, md2, m10, content1), content[n0] = content1[n0], (∅)[m] = mkientry(boolvar0, mkinode(m3, md0, boolvar, m4, m5, m6)), pcache[datakey(m, n)] = mkpentry(true, buf), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), n0 ∈ content1, datakey(m, n) ∈ pcache, m ∈ files1, m ∈ files0, n0 ∈ content1 ⊕ mkcontent(m, pcache0), n0 ∈ content, ∀ ino0. (ino0 ∈ files0 ↔ ino0 ∈ files1) ∧ (ino0 ∈ files0 → ((files0 ⊕ pcache) ⊕ icache)[ino0] = ((files1 ⊕ pcache0) ⊕ icache)[ino0]) ⊦ (content1 ⊕ mkcontent(m, pcache0))[n0] = content[n, buf][n0], datakey(m, n0) = datakey(m, n), datakey(m, n0) ∈ pcache, m ∈ icache, datakey(m, n0) ∈ pcache0, n0 ∈ mkcontent(m, pcache0)

Rule argument

spec: cache-base name: at-overwrite-content-new seq: ⊦ n ∈ content1 → (content0 ⊕ content1)[n] = content1[n] subst: [n, content1, content0] → [n0, mkcontent(m, pcache0), content1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ mkcontent(ino, pcache)[n] = pcache[datakey(ino, n)].page; (s)% ⊦ ¬ key ∈ pcache → pcache[key] = (∅)[key]; (s)% ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache; (s) Used terms: n0, mkcontent(m, pcache0), content1