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Proof step 507 from proof fsync-pages-keep-abs (previous step)

# 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), (∅)[m] = mkientry(boolvar0, mkinode(m3, md0, boolvar, 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, ⌊err0⌋ ⊦ m ∈ icache, datakey(m, n0) ∈ pcache, (n0 ∈ content ↔ n0 ∈ content[n, buf] ⊕ mkcontent(m, pcache)) ∧ (n0 ∈ content → content[n0] = (content[n, buf] ⊕ mkcontent(m, pcache))[n0])

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 508:
# buf = VFS_PAGE_SIZE, n0 ∈ content ↔ n0 ∈ content1 ⊕ mkcontent(m, pcache0), files0[m] = mkfile(m9, md2, m10, content), files1[m] = mkfile(m9, md2, m10, content1), (∅)[m] = mkientry(boolvar0, mkinode(m3, md0, boolvar, m4, m5, m6)), pcache[datakey(m, n)] = mkpentry(true, buf), content[n0] = (content1 ⊕ mkcontent(m, pcache0))[n0], n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), datakey(m, n) ∈ pcache, m ∈ files1, m ∈ files0, n0 ∈ mkcontent(m, pcache0), ⌊err0⌋ ⊦ datakey(m, n0) ∈ pcache, m ∈ icache, (n0 ∈ content ↔ n0 ∈ content[n, buf] ⊕ mkcontent(m, pcache)) ∧ (n0 ∈ content → content[n0] = (content[n, buf] ⊕ mkcontent(m, pcache))[n0])
Proof step 518:
# buf = VFS_PAGE_SIZE, n0 ∈ content ↔ n0 ∈ content1 ⊕ mkcontent(m, pcache0), files0[m] = mkfile(m9, md2, m10, content), files1[m] = mkfile(m9, md2, m10, content1), (∅)[m] = mkientry(boolvar0, mkinode(m3, md0, boolvar, m4, m5, m6)), pcache[datakey(m, n)] = mkpentry(true, buf), content[n0] = (content1 ⊕ mkcontent(m, pcache0))[n0], n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), datakey(m, n) ∈ pcache, m ∈ files1, m ∈ files0, ⌊err0⌋ ⊦ datakey(m, n0) ∈ pcache, m ∈ icache, n0 ∈ mkcontent(m, pcache0), (n0 ∈ content ↔ n0 ∈ content[n, buf] ⊕ mkcontent(m, pcache)) ∧ (n0 ∈ content → content[n0] = (content[n, buf] ⊕ mkcontent(m, pcache))[n0])

Rule argument

fma: n0 ∈ mkcontent(m, pcache0)

Additional information

Used formulas: n0 ∈ mkcontent(m, pcache0)