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Proof step 42 from proof middle-coef-larger-strongest (previous step)

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 ⊦ ∀ i0. i0 ∈ countFun(0, 2 * i, λ j. binom_coef(2 * i, j)) → i0 ≤ binom_coef(2 * i, i)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 43:
4 ^ i = Σ countFun(0, 2 * i, λ j. binom_coef(2 * i, j)), i0 ∈ countFun(0, 2 * i, λ j. binom_coef(2 * i, j)), binom_coef(2 * i, i) ∈ 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) < i0 ⊦

Rule argument

Additional information

Used simplifier rules: lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs