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Proof step 9 from proof lebsize-2page-size-le (previous step)

PAGES_PER_LEB * EB_PAGE_SIZE < m, m + 2 * EB_PAGE_SIZE ≤ n, n ≤ (PAGES_PER_LEB + 2) * EB_PAGE_SIZE, m + 2 * EB_PAGE_SIZE ≤ (PAGES_PER_LEB + 2) * EB_PAGE_SIZE ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: nat-mult name: dist seq: ⊦ m0 * (m + n) = m0 * m + m0 * n subst: [n, m, m0] → [2, PAGES_PER_LEB, EB_PAGE_SIZE] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%mult-c: ⊦ m * n = n * m; from specification nat-mult Used terms: 2, PAGES_PER_LEB, EB_PAGE_SIZE