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Theorem max_exp-divides

⊦ 0 < j ∧ prime(i) → i ^ max_exp(i, j) | j ∧ ¬ i | j / i ^ max_exp(i, j)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 6
Proof steps: 9
Used lemmas: product-pot-rec, max_exp-def,
Used spec theorems:
Used simplifier rules:
- int-abs/forward-le-05
- list-perm/intlista/notin
- int-gcd/div-one
- int-div/one
- int-abs/lels-01
- int-basic1/two-ls
- intlist/prod-empty
- int-gcd/prime-divides-one
- int-abs/forward-le-01
- intlist/all_prime_divisors-in-01
- intlist/all_prime_divisors-product-del
- oelem/intlista/lel
- int-mult/Mult-zero
- int-mult/associativity
- int-mult/commutativity
- intlist/all_prime_divisors-base
- list-perm/intlista/oc-e
- int-pot/Pot-zero