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Proof step 15 from proof pot2-est-mult8 (previous step)

2 * (i1 + 7) < 8 + i1, 2 * (i1 + 7) ≤ 16 * 2 ^ i1, 16 * 2 ^ i1 < 8 + 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

Rule argument

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

Additional information

Used simplifier rules: associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%numls-03: ⊦ (* i2) * i + j < i + j0 ↔ (i2 - 1) * i + j < j0; from specification int-mult%one: ⊦ 1 * i = i; from specification int-mult%numls-03: ⊦ i + (* j) < (* j0) ↔ i < j0 - j; from specification int-abs%zero-gels: ⊦ i < 0 ∧ 0 ≤ j → ¬ j < i; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: 2, 7, i1