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Proof step 31 from proof prime-product (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: ple-pos-better seq: 0 ≤ i, 0 ≤ j, i ≤ i0, j ≤ j0 ⊦ i * j ≤ i0 * j0 subst: [j0, i0, j, i] → [4 ^ j, 4 ^ (j + 1), Π ints0, Π ints1] flags: rewrite

Additional information

Used simplifier rules: lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%primes-product-not-neg: ⊦ primes(ints) → ¬ Π ints < 0; from specification intlist Used terms: 4 ^ j, 4 ^ (j + 1), Π ints0, Π ints1