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Proof step 3 from proof middle-coef-larger-strongest (previous step)

⊦ 0 ≤ j → (i + i0) ^ j = Σ countFun(0, j, λ j0. binom_coef(j, j0) * i ^ j0 * i0 ^ (j - j0))

Lemma Binom-theorem-countFun