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Proof step 19 from proof pot2-est-mult8 (previous step)

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 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult name: ls-same-06 seq: ⊦ i + j * j0 < j ↔ i + j * (j0 - 1) < 0 subst: [i, j0, j] → [6, 2, i1] flags: <all paths>

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% ⊦ 1 * i = i; (s)% ⊦ 0 ≤ i ∧ 0 ≤ j → ¬ i + j < 0; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: 6, 2, i1