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Proof step 26 from proof bertrand-middle-coef-smaller (previous step)

i0 ∈ all_prime_divisors(binom_coef(2 * i, i)), all_prime_divisors(binom_coef(2 * i, i)) = ints + ints0 + (i0 ' + ints3) + ints2, Π ints * Π ints0 * (i0 * Π ints3) * Π ints2 = binom_coef(2 * i, i), 0 < Π ints0, 0 < Π ints, 0 < i, i0 ≤ i, (2 * i) / 3 < i0, 4 ^ ((2 * i) / 3) < Π ints0 * i0 * Π ints3, 0 ≤ Π ints, 0 ≤ Π ints2, (2 * i) ^ (sqrt(2 * i) - 1) * 4 ^ ((2 * i) / 3) < Π ints * Π ints0 * i0 * Π ints3, 2 < i, 0 < Π ints2, 0 < i0 * Π ints3, ∀ j. j ∈ ints0 → sqrt(2 * i) < j ∧ j ≤ (2 * i) / 3, ∀ j. j ∈ ints → j ≤ sqrt(2 * i), ∀ j. j ∈ ints2 → i < j ∧ j ≤ 2 * i, ∀ j. j = i0 ∨ j ∈ ints3 → (2 * i) / 3 < j ∧ j ≤ i ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: forward-le: ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward) from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%all_prime_divisors-in-01: ⊦ j ∈ all_prime_divisors(i) ↔ prime(j) ∧ j | i ∧ 2 ≤ i; from specification intlist