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Proof step 257 from proof refine-truncate (previous step)

files0[ino2] = mkfile(m2 * VFS_PAGE_SIZE + n0, md0, # links(ino2, dirs), content0), root.dir?, m1 * VFS_PAGE_SIZE < n, n1 < VFS_PAGE_SIZE, dom of < ino3, m1 * VFS_PAGE_SIZE + n1 < n, n0 < VFS_PAGE_SIZE, m2 * VFS_PAGE_SIZE + n0 < n, m1 * VFS_PAGE_SIZE < m2 * VFS_PAGE_SIZE + n0, m1 * VFS_PAGE_SIZE + 1 < n, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files0[ino2, mkfile(n, md0, # links(ino2, dirs), content0 upto (m2 * VFS_PAGE_SIZE + n0))]), 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 (m2 * VFS_PAGE_SIZE + n0))]), of-cons(of, dirs, files0), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files0), ROOT_INO ∈ dirs, ino2 ∈ files0, m1 ∈ content0, m2 * VFS_PAGE_SIZE + n0 ≤ m1 * VFS_PAGE_SIZE + n1, psynced0 → asynced0 ⊦ n1 = 0, zero = content0[m1][n1], root[path].dir?, ino2 ∈ dirs, n0 ≠ 0 ∧ m2 ∈ content0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 258:
⊦ m ≤ n → (n ≤ m ↔ m = n)
Proof step 259:
files0[ino2] = mkfile(m2 * VFS_PAGE_SIZE + n0, md0, # links(ino2, dirs), content0), root.dir?, m1 * VFS_PAGE_SIZE + 1 < n, m1 * VFS_PAGE_SIZE < m2 * VFS_PAGE_SIZE + n0, m2 * VFS_PAGE_SIZE + n0 < n, n0 < VFS_PAGE_SIZE, m1 * VFS_PAGE_SIZE + n1 < n, dom of < ino3, n1 < VFS_PAGE_SIZE, m1 * VFS_PAGE_SIZE < n, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files0), afs-cons(dirs, files0[ino2, mkfile(n, md0, # links(ino2, dirs), content0 upto (m2 * VFS_PAGE_SIZE + n0))]), 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 (m2 * VFS_PAGE_SIZE + n0))]), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files0), m1 ∈ content0, ino2 ∈ files0, ROOT_INO ∈ dirs, m2 * VFS_PAGE_SIZE + n0 ≤ m1 * VFS_PAGE_SIZE + n1, psynced0 → asynced0 ⊦ n1 = 0, zero = content0[m1][n1], root[path].dir?, ino2 ∈ dirs, m1 * VFS_PAGE_SIZE + n1 ≤ m2 * VFS_PAGE_SIZE + n0, n0 ≠ 0 ∧ m2 ∈ content0

Rule argument

spec: nat name: anti seq: ⊦ m ≤ n → (n ≤ m ↔ m = n) subst: [m, n] → [m1 * VFS_PAGE_SIZE + n1, m2 * VFS_PAGE_SIZE + n0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n0 < n ∧ n1 < n → (m * n + n0 = m0 * n + n1 ↔ m = m0 ∧ n0 = n1); (ws)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: m1 * VFS_PAGE_SIZE + n1, m2 * VFS_PAGE_SIZE + n0