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Proof step 5 from proof BertrandsPostulate (previous step)

∃ 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), 2 < i, 0 < i ⊦ ∃ j. prime(j) ∧ i < j ∧ j ≤ 2 * i

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
all_prime_divisors(binom_coef(2 * i, i)) = ints2 + ints1 + ints0 + ints, 0 < i, 2 < i, ∀ j. j ∈ ints → i < j ∧ j ≤ 2 * i, ∀ j. j ∈ ints0 → (2 * i) / 3 < j ∧ j ≤ i, ∀ j. j ∈ ints1 → sqrt(2 * i) < j ∧ j ≤ (2 * i) / 3, ∀ j. j ∈ ints2 → j ≤ sqrt(2 * i) ⊦ ∃ j. prime(j) ∧ i < j ∧ j ≤ 2 * i

Rule argument

Additional information

Used simplifier rules: numlslsdel-01: i0 ≠ 0, i0 < i ⊦ (* i) < j → (* i0) < j; from specification int-basic1%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1