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Proof step 5 from proof prime-product (previous step)

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 ⊦ i ≤ 2, ints = [], dups(ints)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
0 < i, 2 < i, 4 ^ i < Π ints, max(ints) ≤ i, primes(ints), ∀ i0, ints. i→n(i0) < i→n(i) → primes(ints) ∧ max(ints) ≤ i0 ∧ ¬ dups(ints) → Π ints ≤ 4 ^ i0 ⊦ ints = [], dups(ints)

Rule argument

Additional information

Used simplifier rules: numlslsdel-01: i0 ≠ 0, i0 < i ⊦ (* i) < j → (* i0) < j; from specification int-basic1%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs