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Proof step 55 from proof readpage-prepost (previous step)

# buf = VFS_PAGE_SIZE, files[m0] = mkfile(n0, md, # links(m0, dirs), content), n1 < VFS_PAGE_SIZE, F(files -- m0), afs-cons(dirs, files), m0 ∈ files ⊦ zero = getpage((n * VFS_PAGE_SIZE + n1) / VFS_PAGE_SIZE, content)[(n * VFS_PAGE_SIZE + n1) % VFS_PAGE_SIZE], n ∈ content

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 56:
# buf = VFS_PAGE_SIZE, files[m0] = mkfile(n0, md, # links(m0, dirs), content), n1 < VFS_PAGE_SIZE, F(files -- m0), afs-cons(dirs, files), m0 ∈ files ⊦ zero = getpage(n, content)[n1], n ∈ content

Rule argument

Additional information

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