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Proof step 62 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) / i) / i) = all_prime_divisors((i * i0) / i) -1l i, prime(i), 2 ≤ i * i0, i | (i * i0) / i, 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) / i) -1l i) + i ', prime(i * i0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: all_prime_divisors-prime: ⊦ prime(i) → all_prime_divisors(i) = i ';%div-mult: ⊦ i | i * j; from specification int-gcd%div-mult-03: j ≠ 0 ⊦ (i * j) / j = i; from specification int-div%div-zero-zero: ⊦ 0 | i ↔ i = 0; from specification int-gcd%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%Mult-zero: ⊦ i * 0 = 0; from specification int-mult