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Proof step 6 from proof two-even (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
2 * i = j1 ^2 + j2 ^2, (j1 - j2) % 2 = 0, j1 + j2 = j * 2 ⊦ i = ((j1 - j2) / 2)^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