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Proof step 4 from proof root-le (previous step)

¬ sqrt(i) ^2 ≤ j, i ≤ j, sqrt(j) < sqrt(i), 0 ≤ i, 0 ≤ j ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
i ≤ j, sqrt(j) < sqrt(i), 0 ≤ i, 0 ≤ j, j < sqrt(i) ^2, i < sqrt(i) ^2, 0 < sqrt(i) ^2 ⊦

Rule argument

Additional information

Used simplifier rules: forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs