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Proof step 8 from proof prime-product-between (previous step)

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)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-pot inst: name: pot-pot-02 seq: ⊦ 0 ≤ j ∧ 0 ≤ j0 → i ^ (j * j0) = (i ^ j) ^ j0 subst: [j0, j, i] → [j, 2, 2] flags: rewrite

Additional information

Used simplifier rules: lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1 Used terms: j, 2, 2