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Proof step 1 from proof prime-product (conclusion)

primes(ints), max(ints) ≤ i, ¬ dups(ints) ⊦ Π ints ≤ 4 ^ i

User applied rule induction

And obtained the following new goals

Proof step 2:
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

Rule argument

indvar: i→n(i) wfpred: <

Additional information

Used simplifier rules: <; (wellfounded) Used terms: i→n(i)