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Proof step 2 from proof coef-le-2pot (previous step)

2 ^ (2 * j) < binom_coef(2 * j + 1, j), 0 < j ⊦

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
⊦ 0 ≤ j → (i + i0) ^ j = Σ countFun(0, j, λ j0. binom_coef(j, j0) * i ^ j0 * i0 ^ (j - j0))
Proof step 4:
0 ≤ 2 * j + 1 → (1 + 1) ^ (2 * j + 1) = Σ countFun(0, 2 * j + 1, λ j0. binom_coef(2 * j + 1, j0) * 1 ^ j0 * 1 ^ (2 * j + 1 - j0)), 2 ^ (2 * j) < binom_coef(2 * j + 1, j), 0 < j ⊦

Rule argument

spec: inst: name: Binom-theorem-countFun seq: ⊦ 0 ≤ j → (i + i0) ^ j = Σ countFun (0, j, λ j0. binom_coef(j, j0) * i ^ j0 * i0 ^ (j - j0)) subst: [j, i, i0] → [2 * j + 1, 1, 1] flags: current, []

Additional information

Used terms: 2 * j + 1, 1, 1