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Proof step 260 from proof refine-truncate (previous step)

files0[ino2] = mkfile(m2 * VFS_PAGE_SIZE + n0, md0, # links(ino2, dirs), content0), root.dir?, m2 * VFS_PAGE_SIZE + n0 < m1 * VFS_PAGE_SIZE + n1, 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, (m2 * VFS_PAGE_SIZE + n0) + 1 < 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, psynced0 → asynced0 ⊦ m2 * VFS_PAGE_SIZE + n0 = m1 * VFS_PAGE_SIZE + n1, n1 = 0, n1 = 1, 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

Rule argument

spec: nat-basic name: addex seq: ⊦ m < n ↔ (∃ m0. m + m0 = n ∧ m0 ≠ 0) subst: [n, m] → [m2 * VFS_PAGE_SIZE + n0, m1 * VFS_PAGE_SIZE] flags: <all paths>

Additional information

Used simplifier rules: lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ m + n < m + n0 ↔ n < n0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m < n → n ≠ 0; (s)% ⊦ n + 0 = n; (s)% ⊦ 0 < m ↔ m ≠ 0; (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ n0 < n → (m * n + n0 = m0 * n ↔ m = m0 ∧ n0 = 0); (ws)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult% ⊦ n0 < n ∧ n1 < n → (m * n + n0 = m0 * n + n1 ↔ m = m0 ∧ n0 = n1); (ws) Used terms: m2 * VFS_PAGE_SIZE + n0, m1 * VFS_PAGE_SIZE