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Proof step 48 from proof pot-root-est (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 49:
⊦ i ^ 2 = i * i
Proof step 50:
2 * i = j * j + j0 ∧ j0 ≤ 2 * j ∧ 0 ≤ j ∧ 0 ≤ j0 ∧ j = sqrt(2 * i), 4 ^ (i / 3) ≤ (2 * i) ^ sqrt(2 * i), 1024 ≤ i, 0 ≤ i, 0 < i ⊦ 2 * i < (j + 1) * (j + 1)

Rule argument

spec: inst: name: pot-square-04 seq: ⊦ i ^ 2 = i * i subst: [i] → [j + 1] flags: rewrite, current

Additional information

Used terms: j + 1