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Theorem all_prime_divisors-in-01

⊦ j ∈ all_prime_divisors(i) ↔ prime(j) ∧ j | i ∧ 2 ≤ i

Type: A user defined theorem
Validity: The proof is valid.
Features: localsimp, simp,
Comment:
Used by: all_prime_divisors-div, all_prime_divisors-in, all_prime_divisors-product-del, all_prime_divisors-rec-02,
Used by units in proved state: int-mod, int-fac,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 5
Proof steps: 9
Used lemmas: all_prime_divisors-prime, all_prime_divisors-base, all_prime_divisors-rec,
Used spec theorems:
- int-gcd/divides-prime
Used simplifier rules: