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Proof step 9 from proof flush-padding-space-aligned (previous step)

EB_PAGE_SIZE = n + m % EB_PAGE_SIZE, is-aligned(n + m % EB_PAGE_SIZE, 2 * NODE_HEADER_SIZE), is-aligned(m, 2 * NODE_HEADER_SIZE) ⊦ is-aligned(n, 2 * NODE_HEADER_SIZE), is-aligned(m % EB_PAGE_SIZE, 2 * NODE_HEADER_SIZE)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: align name: is-aligned-is-aligned-mod seq: n ≠ 0, n0 ≠ 0 ⊦ is-aligned(m, n) ∧ is-aligned(n0, n) → is-aligned(m % n0, n) subst: [n, n0, m] → [2 * NODE_HEADER_SIZE, EB_PAGE_SIZE, m] flags: <all paths>

Additional information

Used simplifier rules: ⊦ 2 * m = 0 ↔ m = 0; (s)% ⊦ NODE_HEADER_SIZE ≠ 0; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult% ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ is-aligned(EB_PAGE_SIZE, 2 * NODE_HEADER_SIZE); (s) Used terms: 2 * NODE_HEADER_SIZE, EB_PAGE_SIZE, m