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Proof step 409 from proof fsync-pages-keep-abs (previous step)

# buf = VFS_PAGE_SIZE, files1[m] = mkfile(m9, md2, m10, content1), pcache[datakey(m, n0)] = mkpentry(boolvar0, content1[n0]), files0[m] = mkfile(m7, md1, m8, content0), pcache[datakey(m, n)] = mkpentry(true, buf), icache[m] = mkientry(boolvar, mkinode(m3, md0, false, m4, m5, m6)), pcache[datakey(m, n), mkpentry(false, buf)][datakey(m, n0)] = mkpentry(boolvar1, buf0), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), datakey(m, n0) ∈ pcache[datakey(m, n), mkpentry(false, buf)], n0 ∈ content1, datakey(m, n0) ∈ pcache, m ∈ files0, m ∈ files1, datakey(m, n) ∈ pcache, m ∈ icache, n0 ∈ content0 ⊕ mkcontent(m, pcache), n0 ∈ content0[n, buf] ⊕ mkcontent(m, pcache[datakey(m, n), mkpentry(false, buf)]), ∀ ino0. (ino0 ∈ files0 ↔ ino0 ∈ files1) ∧ (ino0 ∈ files0 → ((files0 ⊕ pcache) ⊕ icache)[ino0] = ((files1 ⊕ pcache0) ⊕ icache)[ino0]) ⊦ content1[n0] = buf0, datakey(m, n0) ∈ pcache0

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: datakey(m, n0) = datakey(m, n)

Additional information

Used simplifier rules: ⊦ key ≠ key0 → pcache[key0, pe][key] = pcache[key]; (s)% ⊦ key ≠ key0 → (key ∈ pcache[key0, pe] ↔ key ∈ pcache); (s)%⊦ mkpentry(boolvar, buf) = mkpentry(boolvar0, buf0) ↔ (boolvar ↔ boolvar0) ∧ buf = buf0; (ws)% ⊦ datakey(m, m0) = datakey(m1, m2) ↔ m = m1 ∧ m0 = m2; (ws)% ⊦ pcache[key, pe][key] = pe; (s)% ⊦ key ∈ pcache[key, pe]; (s) Used formulas: datakey(m, n0) = datakey(m, n)