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Proof step 8 from proof pot-square-est-01 (previous step)

4 ^ (i1 + 1) ≤ (i1 + 1) * (i1 + 1), ~1 ≤ i1, ∀ i0. i→n(i0) < i→n(i1 + 1) → 4 ^ i0 ≤ i0 * i0 ∧ 0 ≤ i0 → false ⊦ 4 ^ i1 ≤ i1 * i1 ∧ 0 ≤ i1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: succ seq: ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j subst: [i, j] → [i1, 4] flags: rewrite, current

Additional information

Used simplifier rules: Pot-neg: ⊦ i < 0 → j ^ i = 1 / j ^ abs(i);%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%mone-08: ⊦ i < 0 → (~1 ≤ i ↔ i = ~1); from specification int-abs%abs-08: ⊦ i < 0 → abs(i) = ~ i; from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: i1, 4