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Proof step 158 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)), pcache[datakey(m, n0)] = mkpentry(boolvar1, 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[n, buf] ⊕ mkcontent(m, pcache[datakey(m, n), mkpentry(false, buf)]), n0 ∈ content1 ⊕ mkcontent(m, pcache0), datakey(m, n0) ∈ pcache, m ∈ files0, m ∈ files1, datakey(m, n) ∈ pcache, n0 ∈ content ⊕ mkcontent(m, pcache), n0 ∈ content1, datakey(m, n0) ∈ pcache[datakey(m, n), mkpentry(false, buf)], ∀ ino0. (ino0 ∈ files0 ↔ ino0 ∈ files1) ∧ (ino0 ∈ files0 → ((files0 ⊕ pcache) ⊕ icache)[ino0] = ((files1 ⊕ pcache0) ⊕ icache)[ino0]) ⊦ (content1 ⊕ mkcontent(m, pcache0))[n0] = (content[n, buf] ⊕ mkcontent(m, pcache[datakey(m, n), mkpentry(false, buf)]))[n0], datakey(m, n0) ∈ pcache0, m ∈ icache, n0 ∈ mkcontent(m, pcache0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 159:
# buf = VFS_PAGE_SIZE, files0[m] = mkfile(m9, md2, m10, content), files1[m] = mkfile(m9, md2, m10, content1), pcache[datakey(m, n0)] = mkpentry(boolvar1, 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 ∈ content[n, buf] ⊕ mkcontent(m, pcache[datakey(m, n), mkpentry(false, buf)]), datakey(m, n0) ∈ pcache[datakey(m, n), mkpentry(false, buf)], n0 ∈ content ⊕ mkcontent(m, pcache), datakey(m, n) ∈ pcache, m ∈ files1, m ∈ files0, datakey(m, n0) ∈ pcache, n0 ∈ content1, ∀ ino0. (ino0 ∈ files0 ↔ ino0 ∈ files1) ∧ (ino0 ∈ files0 → ((files0 ⊕ pcache) ⊕ icache)[ino0] = ((files1 ⊕ pcache0) ⊕ icache)[ino0]) ⊦ content1[n0] = (content[n, buf] ⊕ mkcontent(m, pcache[datakey(m, n), mkpentry(false, buf)]))[n0], m ∈ icache, datakey(m, n0) ∈ pcache0

Rule argument

Additional information

Used simplifier rules: ⊦ n ∈ mkcontent(ino, pcache) ↔ datakey(ino, n) ∈ pcache; (s)% ⊦ n ∈ content0 ⊕ content1 ↔ n ∈ content0 ∨ n ∈ content1; (ws)% ⊦ ¬ n ∈ content1 → (content0 ⊕ content1)[n] = content0[n]; (s)