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Proof step 5 from proof root-le (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
sqrt(j) < sqrt(i), j < sqrt(i) ^2, i < sqrt(i) ^2, 0 < sqrt(i) ^2, i ≤ j, 0 ≤ i, 0 ≤ j ⊦

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% ⊦ i ≤ j ↔ ¬ j < i; (ss)