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Proof step 19 from proof bertrand-middle-coef-smaller (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: inst: name: bertrand-middle-primes seq: ∀ j. j ∈ ints0 → sqrt(2 * i) < j ∧ j ≤ (2 * i) / 3, all_prime_divisors(binom_coef(2 * i, i)) = ints + ints0 + ints1, 2 < i ⊦ Π ints0 ≤ 4 ^ ((2 * i) / 3) subst: [ints0, i, ints, ints1] → [ints0, i, ints, ints2] flags: current, []

Additional information

Used simplifier rules: lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs Used terms: ints0, i, ints, ints2