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Proof step 4 from proof headersize2-mod-pagesize-is-0 (previous step)

(2 * NODE_HEADER_SIZE) % EB_PAGE_SIZE = 0, is-aligned(EB_PAGE_SIZE, 2 * NODE_HEADER_SIZE) ⊦ EB_PAGE_SIZE = 2 * NODE_HEADER_SIZE

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
m ≠ 0 ⊦ is-aligned(n, m) ↔ (∃ n0. n = n0 * m)
Proof step 6:
(2 * NODE_HEADER_SIZE) % EB_PAGE_SIZE = 0, ∃ n0. EB_PAGE_SIZE = n0 * 2 * NODE_HEADER_SIZE ⊦ 2 * NODE_HEADER_SIZE = 0, EB_PAGE_SIZE = 2 * NODE_HEADER_SIZE

Rule argument

spec: align name: is-aligned-elim seq: m ≠ 0 ⊦ is-aligned(n, m) ↔ (∃ n0. n = n0 * m) subst: [m, n] → [2 * NODE_HEADER_SIZE, EB_PAGE_SIZE] flags: <all paths>

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 Used terms: 2 * NODE_HEADER_SIZE, EB_PAGE_SIZE