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Proof step 12 from proof pot-square-est-02 (previous step)

(i1 + 1) * (i1 + 1) * 4 < (2 + i1) * (2 + i1), (i1 + 1) * (i1 + 1) * 4 < 4 ^ i1 * 4, 4 ^ i1 * 4 ≤ (2 + i1) * (2 + i1), 0 ≤ i1, (i1 + 1) * (i1 + 1) < 4 ^ i1, 1 < i1, 0 < i1, ∀ i0. i→n(i0) < i→n(i1 + 1) → 4 ^ i0 ≤ (i0 + 1) * (i0 + 1) ∧ 0 < i0 ∧ 1 < i0 → false ⊦

User applied rule cut formula

And obtained the following new goals

Proof step 13:
(2 + i1) * (2 + i1) = i1 * i1 + 4 * i1 + 4, (i1 + 1) * (i1 + 1) * 4 < (2 + i1) * (2 + i1), (i1 + 1) * (i1 + 1) * 4 < 4 ^ i1 * 4, 4 ^ i1 * 4 ≤ (2 + i1) * (2 + i1), 0 ≤ i1, (i1 + 1) * (i1 + 1) < 4 ^ i1, 1 < i1, 0 < i1, ∀ i0. i→n(i0) < i→n(i1 + 1) → 4 ^ i0 ≤ (i0 + 1) * (i0 + 1) ∧ 0 < i0 ∧ 1 < i0 → false ⊦
Proof step 27:
(i1 + 1) * (i1 + 1) * 4 < (2 + i1) * (2 + i1), (i1 + 1) * (i1 + 1) * 4 < 4 ^ i1 * 4, 4 ^ i1 * 4 ≤ (2 + i1) * (2 + i1), 0 ≤ i1, (i1 + 1) * (i1 + 1) < 4 ^ i1, 1 < i1, 0 < i1, ∀ i0. i→n(i0) < i→n(i1 + 1) → 4 ^ i0 ≤ (i0 + 1) * (i0 + 1) ∧ 0 < i0 ∧ 1 < i0 → false ⊦ (2 + i1) * (2 + i1) = i1 * i1 + 4 * i1 + 4

Rule argument

fma: (2 + i1) * (2 + i1) = i1 * i1 + 4 * i1 + 4

Additional information

Used formulas: (2 + i1) * (2 + i1) = i1 * i1 + 4 * i1 + 4