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Proof step 244 from proof refine-truncate (previous step)

files0[ino2] = mkfile(m0, md0, # links(ino2, dirs), content0), root.dir?, dom of < ino3, n0 < n, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files0[ino2, mkfile(n, md0, # links(ino2, dirs), content0 upto min(n, m0))]), afs-cons(dirs, files0), fids-cons(root, abs-files(files0), abs-of(of)), ispath(path, ROOT_INO, ino2, dirs, files0), of-cons(of, dirs, files0[ino2, mkfile(n, md0, # links(ino2, dirs), content0 upto min(n, m0))]), of-cons(of, dirs, files0), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files0), ROOT_INO ∈ dirs, ino2 ∈ files0, psynced0 → asynced0 ⊦ (m0 ≤ n0 ⊃ zero;(n0 / VFS_PAGE_SIZE ∈ content0 ⊃ content0[n0 / VFS_PAGE_SIZE];zeropage)[n0 % VFS_PAGE_SIZE]) = getpage(n0 / VFS_PAGE_SIZE, content0 upto min(n, m0))[n0 % VFS_PAGE_SIZE], root[path].dir?, ino2 ∈ dirs, m0 ≤ n ∧ m0 % VFS_PAGE_SIZE ≠ 0 ∧ m0 / VFS_PAGE_SIZE ∈ content0

User applied rule insert elim lemma

And obtained the following new goals

Proof step 245:
files0[ino2] = mkfile(m0, md0, # links(ino2, dirs), content0), n0 = m1 * VFS_PAGE_SIZE + n1, root.dir?, n0 < n, dom of < ino3, n1 < VFS_PAGE_SIZE, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files0), afs-cons(dirs, files0[ino2, mkfile(n, md0, # links(ino2, dirs), content0 upto min(n, m0))]), fids-cons(root, abs-files(files0), abs-of(of)), ispath(path, ROOT_INO, ino2, dirs, files0), of-cons(of, dirs, files0), of-cons(of, dirs, files0[ino2, mkfile(n, md0, # links(ino2, dirs), content0 upto min(n, m0))]), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files0), ino2 ∈ files0, ROOT_INO ∈ dirs, psynced0 → asynced0 ⊦ (m0 ≤ n0 ⊃ zero;(m1 ∈ content0 ⊃ content0[m1];zeropage)[n1]) = getpage(m1, content0 upto min(n, m0))[n1], VFS_PAGE_SIZE = 0, root[path].dir?, ino2 ∈ dirs, m0 ≤ n ∧ m0 % VFS_PAGE_SIZE ≠ 0 ∧ m0 / VFS_PAGE_SIZE ∈ content0

Rule argument

spec: nat-div name: div-elim seq: n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n subst: [m, n, m0, n0] → [n0, VFS_PAGE_SIZE, m0, n1]

Additional information

Used simplifier rules: ⊦ VFS_PAGE_SIZE ≠ 0; (s)%n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n; (elim) Used terms: n0, VFS_PAGE_SIZE, m0, n1