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Proof step 1 from proof Binom-theorem (conclusion)

⊦ 0 ≤ j → (i + i0) ^ j = Σ binom_list(i, i0, j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ binom_list(i, i0, j) = countFun(0, j, λ j0. binom_coef(j, j0) * i ^ j0 * i0 ^ (j - j0))
Proof step 3:
⊦ 0 ≤ j → (i + i0) ^ j = Σ countFun(0, j, λ j0. binom_coef(j, j0) * i ^ j0 * i0 ^ (j - j0))

Rule argument

spec: inst: name: binomlist-def2 seq: ⊦ binom_list(i, i0, j) = countFun (0, j, λ j0. binom_coef(j, j0) * i ^ j0 * i0 ^ (j - j0)) subst: [j, i0, i] → [j, i0, i] flags: rewrite, current

Additional information

Used terms: j, i0, i