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Proof step 16 from proof pot2-est-mult8 (previous step)

8 * 2 ^ i1 * 2 < 8 + i1, 2 * (i1 + 7) < 8 + i1, 2 * (i1 + 7) ≤ 16 * 2 ^ i1, 0 ≤ i1, i1 + 7 ≤ 8 * 2 ^ i1, ∀ i0. i→n(i0) < i→n(i1 + 1) → 8 * 2 ^ i0 < i0 + 7 ∧ 0 ≤ i0 → false ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ (i + i0) * j = i * j + i0 * j
Proof step 18:
i1 * 2 + 7 * 2 < 8 + i1, 8 * 2 ^ i1 * 2 < 8 + i1, i1 + 7 ≤ 8 * 2 ^ i1, 0 ≤ i1, i1 * 2 + 7 * 2 ≤ 16 * 2 ^ i1, ∀ i0. i→n(i0) < i→n(i1 + 1) → 8 * 2 ^ i0 < i0 + 7 ∧ 0 ≤ i0 → false ⊦

Rule argument

spec: int-mult name: dist-lsplit seq: ⊦ (i + i0) * j = i * j + i0 * j subst: [j, i0, i] → [2, 7, i1] flags: <all paths>

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: 2, 7, i1