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Proof step 3 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 ⊦ dups(ints)

User applied rule cut formula

And obtained the following new goals

Proof step 4:
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 ⊦ ints = [], dups(ints)

Rule argument

fma: ints = []

Additional information

Used simplifier rules: max-empty: ⊦ max([]) = 0; from specification intlist%prod-empty: ⊦ Π [] = 1; from specification intlist%lsone: ⊦ i < 1 ↔ i ≤ 0; from specification int-abs%pot-lez: ⊦ 0 < i → (i ^ j ≤ 0 ↔ i ^ j = 0); from specification int-pot%pot-zero-01: ⊦ 0 < i → (i ^ j = 0 ↔ j < 0 ∧ 1 < i); from specification int-pot%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs Used formulas: ints = []