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Proof step 10 from proof middle-coef-larger-strongest (previous step)

4 ^ i = Σ countFun(0, 2 * i, λ j. binom_coef(2 * i, j)), binom_coef(2 * i, i) * 2 * i < 4 ^ i, 0 < i, 0 ≤ i ⊦

User applied rule cut formula

And obtained the following new goals

Proof step 11:
binom_coef(2 * i, i) ∈ countFun(0, 2 * i, λ j. binom_coef(2 * i, j)), 4 ^ i = Σ countFun(0, 2 * i, λ j. binom_coef(2 * i, j)), binom_coef(2 * i, i) * 2 * i < 4 ^ i, 0 < i, 0 ≤ i ⊦
Proof step 45:
4 ^ i = Σ countFun(0, 2 * i, λ j. binom_coef(2 * i, j)), binom_coef(2 * i, i) * 2 * i < 4 ^ i, 0 < i, 0 ≤ i ⊦ binom_coef(2 * i, i) ∈ countFun(0, 2 * i, λ j. binom_coef(2 * i, j))

Rule argument

fma: binom_coef(2 * i, i) ∈ countFun(0, 2 * i, λ j. binom_coef(2 * i, j))

Additional information

Used formulas: binom_coef(2 * i, i) ∈ countFun(0, 2 * i, λ j. binom_coef(2 * i, j))