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Proof step 21 from proof middle-coef-larger-strongest (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

spec: intlist inst: name: sum-all-elems-le seq: ∀ i. i ∈ ints → i ≤ i0 ⊦ Σ ints ≤ i0 * n→i(# ints) subst: [ints, i0] → [countFun(1, 2 * i - 1, λ j. binom_coef(2 * i, j)), binom_coef(2 * i, i)] flags: []

Additional information

Used terms: countFun(1, 2 * i - 1, λ j. binom_coef(2 * i, j)), binom_coef(2 * i, i)