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Proof step 49 from proof two-even (previous step)

2 * i = ((2 * i1 + 1) + j2)^2 + j2 ^2, 2 * (j2 + i1) = 2 * i0 ⊦ 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 50:
2 * i = ((2 * i1 + 1) + j2)^2 + j2 ^2 ⊦ i = ((2 * i1 + 1) / 2)^2 + ((2 * j2 + 2 * i1 + 1) / 2)^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%eq-pos: ⊦ 0 < i → (i * j = i * j0 ↔ j = j0); from specification int-mult