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Proof step 147 from proof refine-truncate (previous step)

VFS_PAGE_SIZE = n0 + m0 % VFS_PAGE_SIZE, files1[ino2] = mkfile(m0, md0, # links(ino2, dirs), content0), m0 % VFS_PAGE_SIZE ≠ 0, root.dir?, dom of < ino3, abs(root, ROOT_INO)(dirs), afs-cons (dirs, files1 [ino2, mkfile(n, md0, # links(ino2, dirs), content0[m0 / VFS_PAGE_SIZE, fill(content0[m0 / VFS_PAGE_SIZE], zero, m0 % VFS_PAGE_SIZE, n0)] upto m0) ]), afs-cons(dirs, files1), fids-cons(root, abs-files(files1), abs-of(of)), ispath(path, ROOT_INO, ino2, dirs, files1), of-cons (of, dirs, files1 [ino2, mkfile(n, md0, # links(ino2, dirs), content0[m0 / VFS_PAGE_SIZE, fill(content0[m0 / VFS_PAGE_SIZE], zero, m0 % VFS_PAGE_SIZE, n0)] upto m0) ]), of-cons(of, dirs, files1), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files1), ROOT_INO ∈ dirs, ino2 ∈ files1, m0 / VFS_PAGE_SIZE ∈ content0, m0 ≤ n, ¬ root[path].dir?, ¬ ino2 ∈ dirs, psynced → asynced0 ⊦ ⟨psynced := ?⟩ ( resize((content0.stream to m0).buf, n) = ((content0[m0 / VFS_PAGE_SIZE, fill(content0[m0 / VFS_PAGE_SIZE], zero, m0 % VFS_PAGE_SIZE, n0)] upto m0).stream to n).buf ∧ (psynced → asynced))

User applied rule insert elim lemma

And obtained the following new goals

Proof step 148:
VFS_PAGE_SIZE = n0 + n1, files1[ino2] = mkfile(m0, md0, # links(ino2, dirs), content0), m0 = m1 * VFS_PAGE_SIZE + n1, root.dir?, dom of < ino3, n1 < VFS_PAGE_SIZE, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files1), afs-cons(dirs, files1[ino2, mkfile(n, md0, # links(ino2, dirs), content0[m1, fill(content0[m1], zero, n1, n0)] upto m0)]), fids-cons(root, abs-files(files1), abs-of(of)), ispath(path, ROOT_INO, ino2, dirs, files1), of-cons(of, dirs, files1), of-cons(of, dirs, files1[ino2, mkfile(n, md0, # links(ino2, dirs), content0[m1, fill(content0[m1], zero, n1, n0)] upto m0)]), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files1), m1 ∈ content0, ino2 ∈ files1, ROOT_INO ∈ dirs, m0 ≤ n, psynced → asynced0 ⊦ ⟨psynced := ?⟩ (resize((content0.stream to m0).buf, n) = ((content0[m1, fill(content0[m1], zero, n1, n0)] upto m0).stream to n).buf ∧ (psynced → asynced)), VFS_PAGE_SIZE = 0, n1 = 0, root[path].dir?, ino2 ∈ dirs

Rule argument

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