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Proof step 8 from proof max_prime_divisor-divides-02 (previous step)

max_prime_divisor(i) * i0 = i, j | (max_prime_divisor(i) * i0) / max_prime_divisor(i), prime(j), 2 ≤ i, 0 ≤ i, 0 < i ⊦ prime(i), j | max_prime_divisor(i) * i0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
j ≠ 0 ⊦ (j * i) / j = i

Rule argument

spec: int-div inst: name: div-mult seq: j ≠ 0 ⊦ (j * i) / j = i subst: [i, j] → [i0, max_prime_divisor(i)] flags: rewrite

Additional information

Used simplifier rules: max_prime_divisor-not-zero: ⊦ ¬ prime(i) ∧ 2 ≤ i → max_prime_divisor(i) ≠ 0;%max_prime_divisor-not-zero: ⊦ ¬ prime(i) ∧ 2 ≤ i → max_prime_divisor(i) ≠ 0;%prime-divides: ⊦ prime(i) → (i | j * j0 ↔ i | j ∨ i | j0);%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: i0, max_prime_divisor(i)