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Proof step 27 from proof bertrand-middle-coef-smaller (previous step)

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, prime(i0), i0 | binom_coef(2 * i, i), 2 ≤ binom_coef(2 * i, i), 0 < binom_coef(2 * i, i), 0 ≤ binom_coef(2 * i, i), ∀ 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 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: bertrand-big-primes seq: ⊦ (2 * i) / 3 < j ∧ j ≤ i ∧ prime(j) ∧ 2 < i → ¬ j | binom_coef(2 * i, i) subst: [i, j] → [i, i0] flags: rewrite, current

Additional information

Used simplifier rules: numlelsdel-01: i0 ≠ 0, i0 ≤ i ⊦ (* i) < j → (* i0) < j; from specification int-abs Used terms: i, i0