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Proof step 2 from proof flush-padding-space-header (previous step)

EB_PAGE_SIZE = n + m % EB_PAGE_SIZE, is-aligned(m, 2 * NODE_HEADER_SIZE) ⊦ 2 * NODE_HEADER_SIZE ≤ n ↔ n ≠ 0, is-aligned(m, EB_PAGE_SIZE)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
n ≠ 0 ⊦ is-aligned(m, n) → (n ≤ m ↔ m ≠ 0)

Rule argument

spec: align name: is-aligned-aligndown-zero-ls seq: n ≠ 0 ⊦ is-aligned(m, n) → (n ≤ m ↔ m ≠ 0) subst: [m, n] → [n, 2 * NODE_HEADER_SIZE] flags: <all paths>

Additional information

Used simplifier rules: flush-padding-space-aligned: ⊦ EB_PAGE_SIZE = n + m % EB_PAGE_SIZE ∧ is-aligned(m, 2 * NODE_HEADER_SIZE) → is-aligned(n, 2 * NODE_HEADER_SIZE);% ⊦ m < n → (n * n0 ≤ m ↔ n0 = 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% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ 2 * m = 0 ↔ m = 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: n, 2 * NODE_HEADER_SIZE