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Proof step 12 from proof two-even (previous step)

2 * i = ((j0 * 2)^2 + 2 * (j0 * 2) * j2 + j2 ^2) + j2 ^2, 2 * j2 + j0 * 2 = j * 2 ⊦ i = j0 ^2 + j ^2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
2 * j2 + j0 * 2 = j * 2, 2 * i = 2 * j2 ^2 + (j0 * 2)^2 + 4 * j0 * j2 ⊦ i = j0 ^2 + j ^2

Rule argument

Additional information

Used simplifier rules: add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-mult-two: ⊦ i + i = 2 * i; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult