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Proof step 12 from proof pot-square-est-01 (previous step)

i1 * i1 * 4 < 4 ^ i1 * 4, 4 ^ i1 * 4 ≤ (i1 + 1) * (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

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

Rule argument

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

Additional information

Used simplifier rules: numls-10: ⊦ 0 < i → ((* i) * j < (* i) * j0 ↔ j < j0); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%numle-10: ⊦ 0 < i → ((* i) * j ≤ (* i) * j0 ↔ j ≤ j0); from specification int-mult%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs Used formulas: i1 * i1 * 4 < (i1 + 1) * (i1 + 1)