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Proof step 17 from proof middle-coef-larger-strongest (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: in-17: ⊦ i ∈ i0 ' ↔ i = i0; from specification list[intlista]%in-append: ⊦ i ∈ ints + ints0 ↔ ¬ ¬(i ∈ ints ∨ i ∈ ints0); from specification list[intlista]%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult%leone: ⊦ 1 ≤ i ↔ 0 < i; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista]%sum-one: ⊦ Σ i ' = i; from specification intlist%sum-app: ⊦ Σ(ints + ints0) = Σ ints + Σ ints0; from specification intlist