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Proof step 2 from proof root-elim (previous step)

0 ≤ i ⊦ ∃ j0. i = sqrt(i) * sqrt(i) + j0 ∧ j0 ≤ 2 * sqrt(i) ∧ 0 ≤ sqrt(i) ∧ 0 ≤ j0

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
⊦ 0 ≤ i → sqrt(i) ^2 ≤ i ∧ i < sqrt(i) +1 ^2
Proof step 4:
0 ≤ i → sqrt(i) ^2 ≤ i ∧ i < sqrt(i) +1 ^2, 0 ≤ i ⊦ ∃ j0. i = sqrt(i) * sqrt(i) + j0 ∧ j0 ≤ 2 * sqrt(i) ∧ 0 ≤ sqrt(i) ∧ 0 ≤ j0

Rule argument

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

Additional information

Used terms: i