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Proof step 11 from proof square-not-neg-05 (previous step)

sqrt(i) = 0, 1 < 1 ^2, 0 < 1 ^2, 0 * 0 < 1 ^2, 0 * 0 < (j + 1) * (j + 1), j * j < 1 ^2, i < 1 ^2, 1 < (j + 1) * (j + 1), i < (j + 1) * (j + 1), 0 < j, 0 < i, 0 < (j + 1) * (j + 1), 0 ≤ i, 0 * 0 ≤ i, j * j ≤ i ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
sqrt(i) = 0, 1 < 1 ^2, 0 < i, 0 < j, i < (j + 1) * (j + 1), 1 < (j + 1) * (j + 1), i < 1 ^2, j * j < 1 ^2, 0 < (j + 1) * (j + 1), 0 < 1 ^2, j * j ≤ i, 0 ≤ i ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; (s)