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Proof step 324 from proof fsync-pages-inv (previous step)

# buf = VFS_PAGE_SIZE, pcache[datakey(m, n0)] = mkpentry(true, buf), files0[m] = mkfile(m1, md0, # links(m, dirs), content), files[m] = mkfile(m3, md, # links(m, dirs), content1), err = err0, n = n0, n0 * VFS_PAGE_SIZE < m2, afs-cons(dirs, files0), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), dcache-cons(dcache, dirs, files0), icache-cons(icache, dirs, files), icache-cons(icache, dirs, files0), pcache-cons(pcache, dirs, files), pcache-cons(pcache0, dirs, files0), synced(dirs, icache, pcache), synced(dirs, icache, pcache0), datakey(m, n0) ∈ pcache, m ∈ files, m ∈ files0, ⌊err0⌋ ⊦ ⟪n := n + 1⟫ ( pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (m2 + VFS_PAGE_SIZE - n * VFS_PAGE_SIZE) + n0 * VFS_PAGE_SIZE < m2 + VFS_PAGE_SIZE)

Heuristic symbolic execution applied rule assign right

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ m * (n + 1) = m * n + m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult% ⊦ m + n - n + n1 = m - n1; (s)% ⊦ n < m → (m - n) + n = m; (s)% ⊦ m < m + n ↔ n ≠ 0; (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)