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Proof step 9 from proof square-neq-any-pos (previous step)

j * j = i * j0 * j0, j < 0, 0 < i ⊦ j = 0, ∃ i0. i = i0 * i0, 0 < ~ j ∧ 0 < j0 ∧ ~ j * ~ j = i * j0 * j0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
j * j = i * j0 * j0, 0 < i, j < 0, j0 < i, j0 ≤ 0 ⊦ j = 0, ∃ i0. i = i0 * i0

Rule argument

Additional information

Used simplifier rules: 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% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ ~ ~ i = i; (s)%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult% ⊦ ~ i * j = ~(i * j); (s)% ⊦ 0 < ~ i ↔ i < 0; (s)