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Proof step 10 from proof pot2-est-mult8 (previous step)

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

User applied rule apply induction

And obtained the following new goals

Rule argument

subst: [i0] → [i1]

Additional information

Used simplifier rules: ⊦ 0 ≤ i → i→n(i + 1) = i→n(i) + 1; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j); (s)% ⊦ 0 ≤ i → abs(i) = i; (s)% ⊦ ¬ i < i; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: i1