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Theorem fermat-pos
⊦ prime(j) ∧ 0 < i → ≡mod(i ^ j, i, j)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
fermat-1
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 15
Proof steps: 27
Used lemmas:
cong-add
,
cong-zero
,
cong-same-add
,
cong-same
,
Used spec theorems:
int-fac
/
Binom-theorem
int-fac
/
binomlist-def2
intlist
/
countFun-rec
intlist
/
countFun-last
int-fac
/
divides-sum
intlist
/
countFun-in
int-fac
/
coef-gcd
int-gcd
/
gcd-com
int-gcd
/
gcd-prime
Used simplifier rules:
int-abs
/
sub-ls-01
intnat
/
abs-pred
int-abs
/
lels-03
int-abs
/
elim-sub
int-abs
/
mone-06
int-gcd
/
prime-not-neg
int-pot
/
one-01
intlist
/
sum-rec
int-fac
/
coef-zero
int-abs
/
anti
int-pot
/
Pot-zero
int-gcd
/
prime-not-neg-01
list
/intlista/
a
intlist
/
sum-one
intlist
/
sum-app
int-mult
/
one
int-fac
/
coef-same
int-basic1
/
forward-pos
int-mult
/
commutativity
int-mult
/
associativity
int-fac
/
prime-divides-pot-01
int-gcd
/
prime-divides
int-abs
/
succ-01
int-abs
/
sub-le-01
int-abs
/
leone
int-basic1
/
ls-01
int-abs
/
lels-01
int-abs
/
numleledel-01
int-abs
/
forward-le-01
int-abs
/
forward-le-05
int-abs
/
le-add-03
int-basic2
/
zero-02
int-abs
/
numls-02
int-abs
/
numle-02
int-abs
/
succ-02
int-basic2
/
add-a
int-basic2
/
add-c
int-abs
/
lels
int-abs
/
bet
int-gcd
/
gcd-add
int-gcd
/
gcd-one-01
int-gcd
/
gcd-com