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Theorem fermat-for-rsa
⊦ prime(j) ∧ j - 1 | i0 ∧ 2 < j ∧ 0 ≤ i ∧ 0 ≤ i0 → (i ^ i0 * i) |%| j = i |%| j
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
RSA-decrypt-ij-vars
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 8
Proof steps: 14
Used lemmas:
mod-mod
,
mod-zero-03
,
mod-mult-01
,
fermat-2-mod
,
mod-mult-law
,
Used spec theorems:
int-mult
/
commutativity
int-pot
/
pot-pot-02
int-gcd
/
gcd-one-prime
int-fac
/
prime-divides-pot-01
int-gcd
/
divides
Used simplifier rules:
int-basic1
/
numlslsdel-01
int-basic1
/
forward-pos
int-abs
/
lels-01
int-mult
/
zero-ge-01
int-abs
/
sub-le
int-abs
/
bet
int-abs
/
sub-eq-01
int-abs
/
forward-le-01
int-mult
/
zero-ge-02
int-abs
/
leone
int-basic2
/
add-c
int-basic2
/
add-a
int-abs
/
sub-le-01
int-mult
/
one
int-abs
/
lels
int-abs
/
anti
oelem
/intlista/
lel
int-pot
/
Pot-zero
int-gcd
/
gcd-one-01
int-abs
/
forward-le-05
int-mult
/
associativity
int-mult
/
commutativity
int-mult
/
Mult-zero