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Proof step 45 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), 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)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-pot inst: name: Pot-pos seq: ⊦ 0 < i → j ^ i = j ^ i -1 * j subst: [i, j] → [i, 4] flags: rewrite

Additional information

Used simplifier rules: sub-pred: ⊦ i -1 = i - 1; from specification int-abs%numls-07: ⊦ (* i1) * j < j ↔ 0 < (1 - i1) * j; from specification int-mult%zero-gr-01: ⊦ i < 0 → (0 < i * j ↔ j < 0); from specification int-mult%notneg-02: ⊦ 0 < i → ¬ i ^ j < 0; from specification int-pot%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: i, 4