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Proof step 18 from proof pot2-est-mult8 (previous step)

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 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
8 * 2 ^ i1 * 2 < 8 + i1, i1 * 2 + 6 < i1, i1 * 2 + 14 ≤ 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 ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ i < j - i0 ↔ i + i0 < j; (s)%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%i < 0 ⊦ (* i) + j = j - ~ i; (s)% ⊦ i + (* j) < i0 + (* j0) ↔ i < i0 + (j0 - j); (s)