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Proof step 43 from proof all_prime_divisors-div (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: transitivity: ⊦ i < i0 ∧ i0 < i1 → i < i1; (forward) from specification oelem[intlista]%prime-one: ⊦ i ≤ 1 → ¬ prime(i); from specification int-gcd%le-same: ⊦ 0 < i → (i * j ≤ i ↔ j ≤ 1); from specification int-mult%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%forward-le: ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward) from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%div-mult: ⊦ i | i * j; from specification int-gcd