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Proof step 11 from proof leb-size-aligned-2-node-header (previous step)

EB_PAGE_SIZE % (2 * NODE_HEADER_SIZE) = 0, LEB_SIZE % EB_PAGE_SIZE = 0 ⊦ LEB_SIZE % (2 * NODE_HEADER_SIZE) = 0

User applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
LEB_SIZE % EB_PAGE_SIZE = 0, EB_PAGE_SIZE = m0 * 2 * NODE_HEADER_SIZE + n0, n0 = 0, n0 < 2 * NODE_HEADER_SIZE ⊦ LEB_SIZE % (2 * NODE_HEADER_SIZE) = 0, 2 * NODE_HEADER_SIZE = 0

Rule argument

spec: nat-div name: div-elim seq: n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n subst: [m, n, m0, n0] → [EB_PAGE_SIZE, 2 * NODE_HEADER_SIZE, m, n]

Additional information

Used simplifier rules: nodeheader-notzero: ⊦ NODE_HEADER_SIZE ≠ 0;% ⊦ 2 * m = 0 ↔ m = 0; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n; (elim) Used terms: EB_PAGE_SIZE, 2 * NODE_HEADER_SIZE, m, n