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Proof step 3 from proof pot-root-est (previous step)

0 < i, 1024 ≤ i, 4 ^ (i / 3) ≤ (2 * i) ^ sqrt(2 * i), 0 ≤ i ⊦

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 4:
⊦ 0 ≤ i → (∃ j, j0. i = j * j + j0 ∧ j0 ≤ 2 * j ∧ 0 ≤ j ∧ 0 ≤ j0 ∧ j = sqrt(i))
Proof step 5:
0 < i, 0 ≤ i, 4 ^ (i / 3) ≤ (2 * i) ^ sqrt(2 * i), 1024 ≤ i, 0 ≤ 2 * i → (∃ j, j0. 2 * i = j * j + j0 ∧ j0 ≤ 2 * j ∧ 0 ≤ j ∧ 0 ≤ j0 ∧ j = sqrt(2 * i)) ⊦

Rule argument

spec: int-square name: root-elim seq: ⊦ 0 ≤ i → (∃ j, j0. i = j * j + j0 ∧ j0 ≤ 2 * j ∧ 0 ≤ j ∧ 0 ≤ j0 ∧ j = sqrt(i)) subst: [i] → [2 * i]

Additional information

Used terms: 2 * i