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Proof step 38 from proof two-even (previous step)

2 * i = (j * 2 - j2)^2 + j2 ^2, (j * 2 - j2) + j2 = j * 2 ⊦ (j * 2 - j2 - j2) % 2 = 0, i = ((j * 2 - j2 - j2) / 2)^2 + j ^2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 39:
2 * i = (j * 2 - j2)^2 + j2 ^2 ⊦ (j * 2 - 2 * j2) % 2 = 0, i = ((j * 2 - 2 * j2) / 2)^2 + j ^2

Rule argument

Additional information

Used simplifier rules: add-mult-two: ⊦ i + i = 2 * i; from specification int-mult%sub-sub: ⊦ i - j - i0 = i - j + i0; from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%eq-pos: ⊦ 0 < i → (i * j = i * j0 ↔ j = j0); from specification int-mult%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%Sub-def: ⊦ i + (j - i) = j; from specification int-abs