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Proof step 11 from proof pot2-est-mult8 (previous step)

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

Rule argument

fma: 2 * (i1 + 7) ≤ 2 * 8 * 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%nummult-modle: 0 < i, i < j, j % i = 0 ⊦ (* i) * i0 ≤ (* j) * j0 ↔ i0 ≤ j / i * j0; from specification int-div%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs Used formulas: 2 * (i1 + 7) ≤ 2 * 8 * 2 ^ i1