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Proof step 52 from proof two-even (previous step)

2 * i = ((2 * i1 + 1)^2 + 2 * (2 * i1 + 1) * j2 + j2 ^2) + j2 ^2 ⊦ i = ((2 * i1 + 1) / 2)^2 + ((2 * j2 + 2 * i1 + 1) / 2)^2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 53:
2 * i = 2 * j2 ^2 + (2 * i1 + 1)^2 + 2 * (2 * i1 + 1) * j2 ⊦ i = ((2 * i1 + 1) / 2)^2 + ((2 * j2 + 2 * i1 + 1) / 2)^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