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Proof step 92 from proof all_prime_divisors-div (previous step)

all_prime_divisors(((i * i0) / max_prime_divisor(i0)) / i) = all_prime_divisors((i * i0) / max_prime_divisor(i0)) -1l i, 0 ≤ i0, 2 ≤ i * i0, 2 ≤ i0, max_prime_divisor(i0) < i * i0, max_prime_divisor(i0) | i * i0, i | (i * i0) / max_prime_divisor(i0), prime(i), 0 < i, 0 < i0, ∀ j. max_prime_divisor(i0) < j ∧ j < i * i0 ∧ prime(j) → ¬ j | i * i0, ∀ j0, i1. i→n(j0) < i→n(i * i0) → i1 | j0 ∧ prime(i1) ∧ 0 < j0 → all_prime_divisors(j0 / i1) = all_prime_divisors(j0) -1l i1 ⊦ all_prime_divisors(i0 / max_prime_divisor(i0)) = all_prime_divisors((i * i0) / max_prime_divisor(i0)) -1l i, prime(i0), prime(i * i0)

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

spec: int-gcd inst: name: prime-ex-max seq: ⊦ ¬ prime(i) ∧ 2 ≤ i → (∃ j. prime(j) ∧ j | i ∧ j < i ∧ (∀ j0. j < j0 ∧ j0 < i ∧ prime(j0) → ¬ j0 | i)) subst: [i] → [i0] flags: []

Additional information

Used terms: i0