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Proof step 9 from proof two-even (previous step)

2 ≠ 0, 2 * i = j1 ^2 + j2 ^2, ∃ j0. j1 - j2 = j0 * 2, j1 + j2 = j * 2 ⊦ i = ((j1 - j2) / 2)^2 + j ^2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
2 * i = (j0 * 2 + j2)^2 + j2 ^2, 2 * j2 + j0 * 2 = j * 2 ⊦ i = j0 ^2 + j ^2

Rule argument

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%one: ⊦ 1 * i = i; from specification int-mult%div-mult-num: j ≠ 0, j0 % j = 0 ⊦ (i * (* j0)) / (* j) = i * j0 / j; from specification int-div%sub-add: ⊦ i + j - i = j; from specification int-abs%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%sub-eq: ⊦ i - j = i0 ↔ i = i0 + j; from specification int-abs