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Proof step 2 from proof coef-product-le (previous step)

binom_coef(2 * j + 1, j) < Π ints, 0 < j, ∀ i. i ∈ ints → prime(i) ∧ j + 2 ≤ i ∧ i ≤ j * 2 + 1 ⊦ dups(ints)

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
¬ dups(ints), ∀ j. j ∈ ints → prime(j) ∧ j | i, 0 < i ⊦ Π ints ≤ i
Proof step 4:
binom_coef(2 * j + 1, j) < Π ints, 0 < j, ∀ i. i ∈ ints → prime(i) ∧ j + 2 ≤ i ∧ i ≤ j * 2 + 1 ⊦ ¬ dups(ints) ∧ (∀ j0. j0 ∈ ints → prime(j0) ∧ j0 | binom_coef(2 * j + 1, j)) ∧ 0 < binom_coef(2 * j + 1, j), dups(ints)

Rule argument

spec: inst: name: primes-divide seq: ¬ dups(ints), ∀ j. j ∈ ints → prime(j) ∧ j | i, 0 < i ⊦ Π ints ≤ i subst: [ints, i] → [ints, binom_coef(2 * j + 1, j)] flags: current, []

Additional information

Used simplifier rules: lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs Used terms: ints, binom_coef(2 * j + 1, j)