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Theorem all_prime_divisors-div
⊦ 0 < j ∧ i | j ∧ prime(i) → all_prime_divisors(j / i) = all_prime_divisors(j) -1l i
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
all_prime_divisors-rec-02
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 59
Proof steps: 105
Used lemmas:
all_prime_divisors-in-01
,
all_prime_divisors-base
,
all_prime_divisors-prime
,
all_prime_divisors-rec
,
Used spec theorems:
list-del
/intlista/
app
int-basic1
/
two-ls
int-div
/
div-lezero
int-gcd
/
div-eq-one
int-gcd
/
prime-divides
int-gcd
/
divides-prime
int-gcd
/
max_prime_divisor-divides-03
list-del
/intlista/
app-01
list
/intlista/
app-03
int-gcd
/
prime-ex-max
int-gcd
/
max_prime_divisor-def
int-div
/
div-mult
int-gcd
/
divides
int-gcd
/
div-mult
list-del
/intlista/
one-01-01
Used simplifier rules:
int-basic1
/
two-ls
list-del
/intlista/
del1-e
int-gcd
/
prime-divides-one
int-div
/
one
int-div
/
div-same
intnat
/
labs
int-abs
/
abs-16
int-gcd
/
max_prime_divisor-not-zero
int-div
/
abs
int-gcd
/
max_prime_divisor-abs-01
int-gcd
/
max_prime_divisor-nle-01
int-gcd
/
max_prime_divisor-nle-zero-01
list-del
/intlista/
app-01
int-gcd
/
prime-small
int-abs
/
lels-01
int-div
/
zero-07
int-abs
/
forward-le-04
int-abs
/
numlsledel
int-div
/
div-zero-05
int-gcd
/
div-not-ls
int-abs
/
numlsledel-01
int-basic1
/
forward-pos
list-del
/intlista/
app
oelem
/intlista/
lel
oelem
/intlista/
irreflexivity
int-gcd
/
prime-one
list
/intlista/
e
list
/intlista/
app-04
int-gcd
/
prime-abs
list-del
/intlista/
in-02-01
list
/intlista/
c-04
int-gcd
/
prime-not-neg-01
int-gcd
/
div-zero-01
int-gcd
/
div-zero-zero
int-abs
/
numleledel-01
int-gcd
/
divides-mult-01
oelem
/intlista/
transitivity
int-mult
/
zero-neq-01
int-mult
/
zero-eq
int-div
/
div-mult-03
list
/intlista/
Nil
int-mult
/
Mult-zero
int-mult
/
eq-pos
int-basic1
/
lst-01
int-mult
/
ls-same-01
int-mult
/
one-01
int-abs
/
bet
int-mult
/
le-same
int-abs
/
lels-02
int-mult
/
ls-pos
int-abs
/
forward-le
int-mult
/
zero-ge
int-abs
/
zero-gels-04
int-mult
/
associativity
int-mult
/
commutativity
int-mult
/
zero-gr
int-gcd
/
div-mult
int-abs
/
lels
int-abs
/
forward-lels
int-abs
/
forward-lsle
int-abs
/
forward-lele
int-mult
/
ls-same
int-abs
/
lsone
int-abs
/
lels-03
int-abs
/
forward-le-05
int-abs
/
forward-le-01
int-gcd
/
max_prime_divisor-divides
list
/intlista/
a
list
/intlista/
app
list-del
/intlista/
one-01
int-gcd
/
max_prime_divisor-prime
int-gcd
/
max_prime_divisor-divides-03
int-gcd
/
max_prime_divisor-ge2