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Proof step 561 from proof fsync-pages-keep-abs (previous step)

# buf = VFS_PAGE_SIZE, n0 ∈ content ⊕ mkcontent(m, pcache) ↔ n0 ∈ content1 ⊕ mkcontent(m, pcache0), 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))[n0] = (content1 ⊕ mkcontent(m, pcache0))[n0], n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), m ∈ icache, datakey(m, n) ∈ pcache, m ∈ files1, m ∈ files0, ⌊err0⌋ ⊦ n0 ∈ mkcontent(m, pcache), (n0 ∈ content1 ⊕ mkcontent(m, pcache0) ↔ n0 ∈ content[n, buf] ⊕ mkcontent(m, pcache)) ∧ (n0 ∈ content1 ⊕ mkcontent(m, pcache0) → (content1 ⊕ mkcontent(m, pcache0))[n0] = (content[n, buf] ⊕ mkcontent(m, pcache))[n0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 562:
# buf = VFS_PAGE_SIZE, n0 ∈ content ↔ n0 ∈ content1 ⊕ mkcontent(m, pcache0), content[n0] = (content1 ⊕ mkcontent(m, pcache0))[n0], 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⌋ ⊦ datakey(m, n0) ∈ pcache, (n0 ∈ content ↔ n0 ∈ content[n, buf] ⊕ mkcontent(m, pcache)) ∧ (n0 ∈ content → content[n0] = (content[n, buf] ⊕ mkcontent(m, pcache))[n0])

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)