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Proof step 12 from proof pot2-est-mult8 (previous step)

2 * (i1 + 7) ≤ 2 * 8 * 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 cut formula

And obtained the following new goals

Proof step 13:
2 * 8 * 2 ^ i1 = 16 * 2 ^ i1, 2 * (i1 + 7) ≤ 2 * 8 * 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 ⊦

Rule argument

fma: 2 * 8 * 2 ^ i1 = 16 * 2 ^ i1

Additional information

Used simplifier rules: associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%eq-pos: ⊦ 0 < i → (i * j = i * j0 ↔ j = j0); from specification int-mult Used formulas: 2 * 8 * 2 ^ i1 = 16 * 2 ^ i1