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Proof step 10 from proof stream-split-partial-lastpage (previous step)

n0 < n + m * VFS_PAGE_SIZE, n < VFS_PAGE_SIZE, n0 / VFS_PAGE_SIZE ∈ content, m * VFS_PAGE_SIZE ≤ n0 ⊦ content[n0 / VFS_PAGE_SIZE][n0 % VFS_PAGE_SIZE] = zero, n = 0, m ∈ content

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: nat name: le-addex seq: ⊦ m ≤ n ↔ (∃ n0. m + n0 = n) subst: [n, m] → [n0, m * VFS_PAGE_SIZE] flags: <all paths>

Additional information

Used simplifier rules: ⊦ VFS_PAGE_SIZE ≠ 0; (s)%n ≠ 0 ⊦ (n0 + m * n) / n = n0 / n + m; (s)%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%n ≠ 0 ⊦ (m + n0 * n) % n = m % n; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%trans: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification nat-basic% ⊦ m < n → m / n = 0; (s)% ⊦ n + 0 = n; (s)% ⊦ ¬ n ∈ content → content[n] = (∅)[n]; (s)% ⊦ m < n → m % n = m; (s)% ⊦ m +1 = m + 1; (s) Used terms: n0, m * VFS_PAGE_SIZE