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Proof step 38 from proof middle-coef-larger-strongest (previous step)

4 ^ i = 2 + Σ countFun(1, 2 * i - 1, λ j. binom_coef(2 * i, j)), 2 ≤ binom_coef(2 * i, i), Σ countFun(1, 2 * i - 1, λ j. binom_coef(2 * i, j)) ≤ binom_coef(2 * i, i) * (2 * i - 1), binom_coef(2 * i, i) ∈ countFun(1, 2 * i - 1, λ j. binom_coef(2 * i, j)), binom_coef(2 * i, i) * 2 * i < 4 ^ i, 0 < i, 0 < binom_coef(2 * i, i), 0 ≤ binom_coef(2 * i, i), ∀ i0. i0 ∈ countFun(1, 2 * i - 1, λ j. binom_coef(2 * i, j)) ∨ i0 = 1 → i0 ≤ binom_coef(2 * i, i) ⊦ i = 0

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: 4 ^ i ≤ binom_coef(2 * i, i) + (2 * i - 1) * binom_coef(2 * i, i)

Additional information

Used formulas: 4 ^ i ≤ binom_coef(2 * i, i) + (2 * i - 1) * binom_coef(2 * i, i)