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Proof step 15 from proof pot-square-est-01 (previous step)

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

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: i1 * i1 * 3 < 2 * i1 + 1

Additional information

Used simplifier rules: numls-05: ⊦ (* i2) * i < i + j0 ↔ (i2 - 1) * i < j0; from specification int-mult%succ-02: ⊦ i < j + 1 ↔ i ≤ j; 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%numls-10: ⊦ 0 < i → ((* i) * j < (* i) * j0 ↔ j < j0); from specification int-mult%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs Used formulas: i1 * i1 * 3 < 2 * i1 + 1