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Proof step 16 from proof prime-product (previous step)

Π ints = Π ints1 * Π ints0, 0 < j, 0 ≤ j, max(ints) ≤ 2 * j + 1, 4 ^ (2 * j + 1) < Π ints, primes(ints), perm(ints, ints1 + ints0), ints0 = [] ∨ j + 1 < min(ints0), ints1 = [] ∨ max(ints1) ≤ j + 1, ∀ i0, ints. i→n(i0) < i→n(j + j + 1) → primes(ints) ∧ max(ints) ≤ i0 ∧ ¬ dups(ints) → Π ints ≤ 4 ^ i0 ⊦ ints = [], dups(ints)

User applied rule cut formula

And obtained the following new goals

Proof step 17:
primes(ints1) ∧ primes(ints0) ∧ ¬ dups(ints1) ∧ ¬ dups(ints0), Π ints = Π ints1 * Π ints0, 0 < j, 0 ≤ j, max(ints) ≤ 2 * j + 1, 4 ^ (2 * j + 1) < Π ints, primes(ints), perm(ints, ints1 + ints0), ints0 = [] ∨ j + 1 < min(ints0), ints1 = [] ∨ max(ints1) ≤ j + 1, ∀ i0, ints. i→n(i0) < i→n(j + j + 1) → primes(ints) ∧ max(ints) ≤ i0 ∧ ¬ dups(ints) → Π ints ≤ 4 ^ i0 ⊦ ints = [], dups(ints)

Rule argument

fma: primes(ints1) ∧ primes(ints0) ∧ ¬ dups(ints1) ∧ ¬ dups(ints0)

Additional information

Used simplifier rules: primes-perm-01: ⊦ ¬ primes(ints1) ∧ primes(ints) → ¬ perm(ints, ints1 + ints0); from specification intlist%a: ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1; from specification list[intlista]%primes-perm-02: ⊦ ¬ primes(ints0) ∧ primes(ints) → ¬ perm(ints, ints1 + ints0); from specification intlist%perm-dups-02: ⊦ ¬ dups(ints) ∧ dups(ints0) → ¬ perm(ints, ints0 + ints1); from specification list-perm[intlista]%perm-dups-03: ⊦ ¬ dups(ints) ∧ dups(ints0) → ¬ perm(ints, ints1 + ints0); from specification list-perm[intlista] Used formulas: primes(ints1) ∧ primes(ints0) ∧ ¬ dups(ints1) ∧ ¬ dups(ints0)