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Proof step 2 from proof bertrand-prime-factors (previous step)

1 < i, 0 < i ⊦ ∃ ints, ints0, ints1, ints2. all_prime_divisors(binom_coef(2 * i, i)) = ints + ints0 + ints1 + ints2 ∧ (∀ j. j ∈ ints → j ≤ sqrt(2 * i)) ∧ (∀ j. j ∈ ints0 → sqrt(2 * i) < j ∧ j ≤ (2 * i) / 3) ∧ (∀ j. j ∈ ints1 → (2 * i) / 3 < j ∧ j ≤ i) ∧ (∀ j. j ∈ ints2 → i < j ∧ j ≤ 2 * i)

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 3:
⊦ ordered≤(all_prime_divisors(i))
Proof step 4:
ordered≤(all_prime_divisors(binom_coef(2 * i, i))), 1 < i, 0 < i ⊦ ∃ ints, ints0, ints1, ints2. all_prime_divisors(binom_coef(2 * i, i)) = ints + ints0 + ints1 + ints2 ∧ (∀ j. j ∈ ints → j ≤ sqrt(2 * i)) ∧ (∀ j. j ∈ ints0 → sqrt(2 * i) < j ∧ j ≤ (2 * i) / 3) ∧ (∀ j. j ∈ ints1 → (2 * i) / 3 < j ∧ j ≤ i) ∧ (∀ j. j ∈ ints2 → i < j ∧ j ≤ 2 * i)

Rule argument

spec: intlist inst: name: all_prime_divisors-ordered seq: ⊦ ordered≤(all_prime_divisors(i)) subst: [i] → [binom_coef(2 * i, i)] flags: []

Additional information

Used terms: binom_coef(2 * i, i)