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Proof step 5 from proof bertrand-big-primes (previous step)

max_exp(j, binom_coef(2 * i, i)) = 0, j | binom_coef(2 * i, i), (2 * i) / 3 < j, j ≤ i, prime(j), 2 < i, 0 < i ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: max_exp-def seq: ⊦ max_exp(i, j) = n→i(#oc(i, all_prime_divisors(j))) subst: [j, i] → [binom_coef(2 * i, i), j] flags: rewrite, current

Additional information

Used simplifier rules: middle-coef-not-one-01: ⊦ 0 < i → ¬ binom_coef(2 * i, i) < 2;%nat2int-02: ⊦ n→i(n) = 0 ↔ n = 0; from specification intnat%oc-zero: ⊦ #oc(i, ints) = 0 ↔ ¬ i ∈ ints; from specification list-perm[intlista]%all_prime_divisors-in-01: ⊦ j ∈ all_prime_divisors(i) ↔ prime(j) ∧ j | i ∧ 2 ≤ i; from specification intlist%lels-01: ⊦ ¬ i ≤ 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: binom_coef(2 * i, i), j