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Theorem prime-fac-divides-not

⊦ prime(i) ∧ j < i ∧ 0 < j → ¬ i | fac(j)

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: max_exp-fac-rec, max_exp-fac-same, middle-coef-divides-not, prime-divides-coef,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 4
Proof steps: 6
Used lemmas: fac-zero, fac-rec,
Used spec theorems:
- int-gcd/prime-divides
Used simplifier rules:
- int-basic1/forward-pos
- int-abs/forward-le-05
- oelem/intlista/transitivity
- int-gcd/div-not-ls
- int-abs/sub-ls
- int-abs/succ-02
- int-basic2/add-a
- int-basic2/add-c
- int-abs/sub-ls-01
- int-abs/lels-01
- int-basic1/ls-01
- int-abs/lels
- int-abs/bet
- int-abs/sub-eq-01
- int-gcd/div-one-pos
- oelem/intlista/lel
- oelem/intlista/irreflexivity
- intnat/abs-pred
- int-abs/lels-03