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Proof step 2 from proof middle-coef-larger-strongest (previous step)

binom_coef(2 * i, i) * 2 * i < 4 ^ i, 0 < i ⊦

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 * i → (1 + 1) ^ (2 * i) = Σ countFun(0, 2 * i, λ j0. binom_coef(2 * i, j0) * 1 ^ j0 * 1 ^ (2 * i - j0)), binom_coef(2 * i, i) * 2 * i < 4 ^ i, 0 < i ⊦

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 * i, 1, 1] flags: current, []

Additional information

Used terms: 2 * i, 1, 1