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Proof step 5 from proof pebsize-simp-ls (previous step)

PEB_SIZE < (PAGES_PER_LEB + 2) * EB_PAGE_SIZE ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ m0 * (m + n) = m0 * m + m0 * n
Proof step 7:
⊦ PEB_SIZE < 2 * EB_PAGE_SIZE + n ↔ LEB_SIZE < n
Proof step 8:
⊦ ¬ LEB_SIZE < PAGES_PER_LEB * EB_PAGE_SIZE

Rule argument

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

Additional information

Used simplifier rules: pebsize-le-2page-size-n: ⊦ PEB_SIZE < 2 * EB_PAGE_SIZE + n ↔ LEB_SIZE < n;%lebsize-simp-ls: ⊦ ¬ LEB_SIZE < PAGES_PER_LEB * EB_PAGE_SIZE;%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%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: EB_PAGE_SIZE, 2, PAGES_PER_LEB