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Theorem cong-crt-01
≡mod(i ^ i0, i, j), ≡mod(i ^ i0, i, j0), prime(j), prime(j0), 0 < i, j ≠ j0, 0 ≤ i0 ⊦ ≡mod(i ^ i0, i, j * j0)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
mod-crt
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 9
Proof steps: 17
Used lemmas:
congmod-def
,
Used spec theorems:
int-gcd
/
divides
int-abs
/
sub-same-01
int-gcd
/
div-mult-01
int-gcd
/
coprime-divides
Used simplifier rules:
int-abs
/
forward-le-05
int-abs
/
forward-le-01
int-gcd
/
div-abs-02
int-abs
/
sub-eq
int-basic2
/
add-in
int-mult
/
Mult-zero
int-mult
/
associativity
int-mult
/
commutativity
int-basic2
/
add-zero
int-basic2
/
add-a
int-basic2
/
add-c
int-mult
/
zero-eq
int-gcd
/
prime-not-neg-01
int-gcd
/
gcd-primes