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Proof step 9 from proof root-elim (previous step)

0 ≤ i, sqrt(i) * sqrt(i) ≤ i, i < (sqrt(i) + 1) * (sqrt(i) + 1), sqrt(i) * sqrt(i) < (sqrt(i) + 1) * (sqrt(i) + 1), 0 < (sqrt(i) + 1) * (sqrt(i) + 1) ⊦ ∃ j0. i = sqrt(i) * sqrt(i) + j0 ∧ j0 ≤ 2 * sqrt(i) ∧ 0 ≤ sqrt(i) ∧ 0 ≤ j0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: root-abs: ⊦ 0 ≤ i → abs(sqrt(i)) = sqrt(i);%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%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%square-ls: ⊦ i * i < j * j ↔ abs(i) < abs(j); from specification int-mult