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Theorem all_prime_divisors-rec-02
⊦ prime(i) ∧ 0 < j → #oc(i, all_prime_divisors(i * j)) = #oc(i, all_prime_divisors(j)) + 1
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
all_prime_divisors-rec-01
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 6
Proof steps: 10
Used lemmas:
all_prime_divisors-in-01
,
all_prime_divisors-prime
,
all_prime_divisors-div
,
Used spec theorems:
list-perm
/intlista/
del1
int-basic1
/
two-ls
Used simplifier rules:
int-abs
/
forward-le-05
int-gcd
/
prime-not-neg-01
int-div
/
div-mult-03
list-perm
/intlista/
oc-zero
nat-basic2
/
one
list-perm
/intlista/
one
int-mult
/
Mult-zero
nat
/
pred-03
nat
/
lels-01
nat-basic1
/
one-01
list-perm
/intlista/
in-05
nat
/
eq-02
nat-basic2
/
c
nat-basic2
/
a
list-perm
/intlista/
notin
list-del
/intlista/
in-02-01
int-abs
/
lels-01
int-gcd
/
div-mult
int-mult
/
eq-one
int-abs
/
abs-16
int-mult
/
associativity
int-mult
/
commutativity
int-mult
/
one-01
int-gcd
/
prime-one
int-mult
/
zero-gr
int-abs
/
lels
int-abs
/
lels-03