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Proof step 42 from proof pot-root-est (previous step)

2 * i = sqrt(2 * i) * sqrt(2 * i) + j0, (2 * i) ^ sqrt(2 * i) < ((sqrt(2 * i) + 1) ^ 2) ^ sqrt(2 * i), 2 * i < (sqrt(2 * i) + 1) ^ 2, j0 ≤ 2 * sqrt(2 * i), 0 ≤ sqrt(2 * i), 0 ≤ j0, 4 ^ (i / 3) ≤ (2 * i) ^ sqrt(2 * i), 1024 ≤ i, 0 ≤ i, 0 < i ⊦ sqrt(2 * i) * sqrt(2 * i) ≤ 2 * i

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 43:
⊦ 0 ≤ i → sqrt(i) ^2 ≤ i ∧ i < sqrt(i) +1 ^2
Proof step 44:
0 ≤ 2 * i → sqrt(2 * i) ^2 ≤ 2 * i ∧ 2 * i < sqrt(2 * i) +1 ^2, 2 * i = sqrt(2 * i) * sqrt(2 * i) + j0, (2 * i) ^ sqrt(2 * i) < ((sqrt(2 * i) + 1) ^ 2) ^ sqrt(2 * i), 2 * i < (sqrt(2 * i) + 1) ^ 2, j0 ≤ 2 * sqrt(2 * i), 0 ≤ sqrt(2 * i), 0 ≤ j0, 4 ^ (i / 3) ≤ (2 * i) ^ sqrt(2 * i), 1024 ≤ i, 0 ≤ i, 0 < i ⊦ sqrt(2 * i) * sqrt(2 * i) ≤ 2 * i

Rule argument

spec: int-square inst: name: Sqrt-def seq: ⊦ 0 ≤ i → sqrt(i) ^2 ≤ i ∧ i < sqrt(i) +1 ^2 subst: [i] → [2 * i] flags: []

Additional information

Used terms: 2 * i