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Proof step 7 from proof prime-product-between (previous step)

0 < j → binom_coef(2 * j + 1, j) ≤ 2 ^ (2 * j), Π ints ≤ binom_coef(2 * j + 1, j), primes(ints), j + 2 ≤ min(ints), max(ints) ≤ j * 2 + 1, 4 ^ j < Π ints, 0 < j, 4 ^ j < binom_coef(2 * j + 1, j) ⊦ dups(ints)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
Π ints ≤ binom_coef(2 * j + 1, j), primes(ints), j + 2 ≤ min(ints), max(ints) ≤ j * 2 + 1, 4 ^ j < Π ints, 0 < j, 4 ^ j < binom_coef(2 * j + 1, j), binom_coef(2 * j + 1, j) ≤ 2 ^ (2 * j), Π ints ≤ 2 ^ (2 * j), 4 ^ j < 2 ^ (2 * j) ⊦ dups(ints)

Rule argument

Additional information

Used simplifier rules: forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs