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Proof step 9 from proof abs-nodes-aligned-2headersize-mod (previous step)

EB_PAGE_SIZE = n + # buf % EB_PAGE_SIZE, abs-nodes(buf, 0, x, lax, false) ⊦ is-aligned(# buf % EB_PAGE_SIZE, 2 * NODE_HEADER_SIZE), is-aligned(n, 2 * NODE_HEADER_SIZE)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
m0 ≠ 0, m1 ≠ 0 ⊦ is-aligned(m0, m1) → (is-aligned(n % m0, m1) ↔ is-aligned(n, m1))

Rule argument

spec: align name: is-aligned-of-mod seq: m0 ≠ 0, m1 ≠ 0 ⊦ is-aligned(m0, m1) → (is-aligned(n % m0, m1) ↔ is-aligned(n, m1)) subst: [m1, m0, n] → [2 * NODE_HEADER_SIZE, EB_PAGE_SIZE, # buf] flags: <all paths>

Additional information

Used simplifier rules: abs-nodes-aligned-2headersize-h: ⊦ abs-nodes(buf, m, x, lax, false) → is-aligned(# buf, 2 * NODE_HEADER_SIZE);% ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ 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% ⊦ is-aligned(EB_PAGE_SIZE, 2 * NODE_HEADER_SIZE); (s) Used terms: 2 * NODE_HEADER_SIZE, EB_PAGE_SIZE, # buf