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Theorem gcd-mod-one
1 < j, 1 < i, gcd(i, j) = 1 ⊦ ∃ i0. (i * i0) % j = 1
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
gcd-mod-one-01
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 8
Proof steps: 13
Used lemmas:
divides
,
gcd-conq-one
,
Used spec theorems:
Used simplifier rules:
int-abs
/
forward-le-05
int-basic1
/
forward-pos
int-abs
/
lels-01
int-basic1
/
ls-01
int-abs
/
sub-eq
int-abs
/
numle-03
int-abs
/
mone-05
int-basic2
/
succ-01
int-div
/
mod-zero-04
int-abs
/
negeq
int-abs
/
abs-08
int-abs
/
abs-neg
int-mult
/
eq-one-neg
int-abs
/
numadd-01
int-mult
/
zero-left
int-abs
/
forward-le-02
int-basic1
/
lf-02
int-basic1
/
trans
int-basic1
/
lf-01
int-abs
/
zero-gels-01
int-mult
/
zero-ls
int-abs
/
anti
int-mult
/
zero-le
int-abs
/
forward-le-01
int-abs
/
lels
int-div
/
mod-mult-pos
int-mult
/
associativity
int-mult
/
commutativity
int-basic2
/
add-a
int-basic2
/
add-c