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Proof step 23 from proof Binom-theorem-countFun (previous step)

⊦ 0 < j1 ∧ j1 ≤ i1 → countFun(j1, i1, λ j0. binom_coef(i1 + 1, j0) * i ^ j0 * i0 ^ (i1 + 1 - j0)) = countFun(j1, i1, λ j0. binom_coef(i1, j0 - 1) * i ^ j0 * i0 ^ (i1 + 1 - j0) + binom_coef(i1, j0) * i ^ j0 * i0 ^ (i1 + 1 - j0))

Lemma countFun-add