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Proof step 31 from proof bertrand-middle-primes (previous step)

all_prime_divisors(binom_coef(2 * i, i)) = ints + ints0 + ints1, 0 < i, 4 ^ ((2 * i) / 3) < Π ints0, 2 < i, (2 * i) / 3 < max(ints0), ∀ j. j ∈ ints0 → sqrt(2 * i) < j ∧ j ≤ (2 * i) / 3 ⊦ dups(ints0)

User applied rule all left

And closed the goal!

Rule argument

pos: left 6 terms: max(ints0) abort: F discard: T computed: T

Additional information

Used simplifier rules: max-in-01: ⊦ max(ints) ∈ ints ↔ ints ≠ []; from specification intlist%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%Nil: ⊦ [] + ints = ints; from specification list[intlista]%a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista]%max-empty: ⊦ max([]) = 0; from specification intlist%div-ls-zero: 0 < j ⊦ i / (* j) < 0 ↔ i + j ≤ 0; from specification int-div%numle-03: ⊦ i + (* j) ≤ (* j0) ↔ i ≤ j0 - j; from specification int-abs%nummult-le-01: ⊦ 0 < i ∧ j < 0 → ((* i) * i0 ≤ (* j) ↔ i0 ≤ (j + 1 - i) / i); from specification int-div%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%zero-gels-02: ⊦ i < 0 ∧ 0 < j → ¬ j ≤ i; from specification int-abs%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: max(ints0)