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Proof step 2 from proof prime-product (previous step)

primes(ints) ∧ max(ints) ≤ i ∧ ¬ dups(ints), ∀ i0, ints. i→n(i0) < i→n(i) → primes(ints) ∧ max(ints) ≤ i0 ∧ ¬ dups(ints) → Π ints ≤ 4 ^ i0 ⊦ Π ints ≤ 4 ^ i

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
primes(ints), max(ints) ≤ i, 4 ^ i < Π ints, ∀ i0, ints. i→n(i0) < i→n(i) → primes(ints) ∧ max(ints) ≤ i0 ∧ ¬ dups(ints) → Π ints ≤ 4 ^ i0 ⊦ dups(ints)

Rule argument

Additional information

Used simplifier rules: lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs