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Theorem cong-crt
≡mod(i, 1, j), ≡mod(i, 1, j0), prime(j), prime(j0), 0 < i, j ≠ j0 ⊦ ≡mod(i, 1, j * j0)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 6
Proof steps: 12
Used lemmas:
congmod-def
,
Used spec theorems:
int-gcd
/
divides
int-gcd
/
divides-mult
int-gcd
/
divides-prime
Used simplifier rules:
int-abs
/
forward-le-05
int-abs
/
abs-16
int-abs
/
abs-09
int-abs
/
forward-le-01
int-abs
/
mone-06
int-abs
/
numls-02
int-basic2
/
add-c
int-basic2
/
add-a
int-basic2
/
add-zero
int-abs
/
numsub
int-abs
/
sub-eq
int-gcd
/
prime-not-neg-01
int-mult
/
commutativity
int-mult
/
associativity
int-gcd
/
prime-divides
int-gcd
/
prime-abs
int-gcd
/
prime-one