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Proof step 17 from proof pot-square-est-01 (previous step)

i1 * i1 * 4 < i1 * i1 + 2 * i1 + 1, i1 * i1 < 4 ^ i1, i1 * i1 * 4 < 4 ^ i1 * 4, i1 * i1 * 3 < 2 * i1 + 1, 0 ≤ i1, 4 ^ i1 * 4 ≤ i1 * i1 + 2 * i1 + 1, ∀ i0. i→n(i0) < i→n(i1 + 1) → 4 ^ i0 ≤ i0 * i0 ∧ 0 ≤ i0 → false ⊦

User applied rule cut formula

And closed the goal!

Rule argument

fma: i1 = 0

Additional information

Used simplifier rules: ⊦ i ≠ j → (i ≤ j ↔ i < j); (s)% ⊦ i * j + i * j0 = i * (j + j0); (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ i < j + 1 ↔ i ≤ j; (s)% ⊦ 0 < i → (i * j ≤ i * i0 ↔ j ≤ i0); (s)% ⊦ 0 < i → (i * j < i * j0 ↔ j < j0); (s)% ⊦ 0 < i ∧ 0 ≤ j → ((* i) * i0 ≤ (* j) ↔ i0 ≤ j / i); (s)% ⊦ i < j → ¬ j < i; (s) Used formulas: i1 = 0