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Proof step 44 from proof prime-product (previous step)

Π ints ≤ 4 ^ (i - 1), primes(ints), max(ints) ≤ i, 4 ^ i < Π ints, 2 < i, 0 < i, even(i), ∀ i0, ints. i→n(i0) < i→n(i) → 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 45:
Π ints ≤ 4 ^ (i - 1), primes(ints), max(ints) ≤ i, 4 ^ i < Π ints, 2 < i, 0 < i, even(i), 4 ^ i < 4 ^ (i - 1), ∀ 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: forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs