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Proof step 12 from proof prime-product (previous step)

∃ ints0, ints1. perm(ints, ints0 + ints1) ∧ (ints0 = [] ∨ max(ints0) ≤ j + 1) ∧ (ints1 = [] ∨ j + 1 < min(ints1)), primes(ints), 4 ^ (2 * j + 1) < Π ints, max(ints) ≤ 2 * j + 1, 0 ≤ j, 0 < j, ∀ i0, ints. i→n(i0) < i→n(j + j + 1) → primes(ints) ∧ max(ints) ≤ i0 ∧ ¬ dups(ints) → Π ints ≤ 4 ^ i0 ⊦ ints = [], dups(ints)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
0 < j, 0 ≤ j, max(ints) ≤ 2 * j + 1, 4 ^ (2 * j + 1) < Π ints, primes(ints), perm(ints, ints1 + ints0), ints0 = [] ∨ j + 1 < min(ints0), ints1 = [] ∨ max(ints1) ≤ j + 1, ∀ i0, ints. i→n(i0) < i→n(j + j + 1) → primes(ints) ∧ max(ints) ≤ i0 ∧ ¬ dups(ints) → Π ints ≤ 4 ^ i0 ⊦ ints = [], dups(ints)

Proof step 12 from proof prime-product (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information