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

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

User applied rule cut formula

And obtained the following new goals

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

Rule argument

fma: (i1 + 1) * (i1 + 1) * 4 < (2 + i1) * (2 + i1)

Additional information

Used simplifier rules: ⊦ 0 < i → (i * j < i * j0 ↔ j < j0); (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ i < j ↔ ¬ j ≤ i; (ss)%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs% ⊦ 0 < i → (i * j ≤ i * i0 ↔ j ≤ i0); (s)% ⊦ i < j → (j ≤ i ↔ false); (as) Used formulas: (i1 + 1) * (i1 + 1) * 4 < (2 + i1) * (2 + i1)