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Proof step 13 from proof square-neq-any-pos (previous step)

0 ≠ j, j * j = i * j0 * j0, 0 < i, 0 ≤ j, j ≠ 0 ∨ j0 ≠ 0 ⊦ 0 < j ∧ 0 < j0, ∃ i0. i = i0 * i0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
j * j = i * j0 * j0, 0 < i, 0 < j, j0 ≤ 0, j0 < i, j0 < j ⊦ 0 = j, ∃ i0. i = i0 * i0

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs