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Proof step 547 from proof fsync-pages-keep-abs (previous step)

# buf = VFS_PAGE_SIZE, n0 ∈ content ⊕ mkcontent(m, pcache) ↔ n0 ∈ content1 ⊕ mkcontent(m, pcache0), 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⌋ , n0 ∈ content1 ⊕ mkcontent(m, pcache0) → (content ⊕ mkcontent(m, pcache))[n0] = (content1 ⊕ mkcontent(m, pcache0))[n0] ⊦ (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 nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 548:
# 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 ∈ content1 ⊕ mkcontent(m, pcache0) → (content ⊕ mkcontent(m, pcache))[n0] = (content1 ⊕ mkcontent(m, pcache0))[n0] ⊦ (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])

Rule argument

fma: (content ⊕ mkcontent(m, pcache))[n0] = (content1 ⊕ mkcontent(m, pcache0))[n0]

Additional information

Used simplifier rules: ⊦ ¬ n ∈ content → content[n] = (∅)[n]; (s) Used formulas: (content ⊕ mkcontent(m, pcache))[n0] = (content1 ⊕ mkcontent(m, pcache0))[n0]