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Proof step 36 from proof middle-coef-larger-strongest (previous step)

4 ^ i = 2 + Σ countFun(1, 2 * i - 1, λ j. binom_coef(2 * i, j)), 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, ∀ 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

Proof step 37:
2 ≤ binom_coef(2 * i, i), 4 ^ i = 2 + Σ countFun(1, 2 * i - 1, λ j. binom_coef(2 * i, j)), 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, ∀ i0. i0 ∈ countFun(1, 2 * i - 1, λ j. binom_coef(2 * i, j)) ∨ i0 = 1 → i0 ≤ binom_coef(2 * i, i) ⊦ i = 0

Rule argument

fma: 2 ≤ binom_coef(2 * i, i)

Additional information

Used simplifier rules: middle-coef-not-one-01: ⊦ 0 < i → ¬ binom_coef(2 * i, i) < 2;%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used formulas: 2 ≤ binom_coef(2 * i, i)