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Theorem abs-pos
⊦ 0 < j → abs(rational(i, j)) = rational(abs(i), j)
Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 16
Proof steps: 26
Used lemmas:
num-zero
,
numerator-pos
,
denominator-zero
,
numerator-zero
,
denominator-pos
,
denum-same
,
num-same-01
,
Equality
,
abs-def
,
Used spec theorems:
int-gcd
/
gcd-abs-rew-01
int-abs
/
Abs-pos
int-div
/
abs
int-abs
/
abs-01
int-gcd
/
gcd-abs
int-gcd
/
gcd-abs-rew-02
Used simplifier rules:
int-abs
/
abs-06
int-gcd
/
gcd-div-gcd-pos
int-div
/
one
int-abs
/
lels-02
int-basic1
/
ls-01
int-abs
/
abs-08
int-div
/
neg-01
int-abs
/
neg-10
int-gcd
/
div-gcd-zero
int-gcd
/
gcd-com
int-gcd
/
div-gcd-not-neg
int-abs
/
lels
int-gcd
/
gcd-abs
int-div
/
abs
int-gcd
/
gcd-zero-zero
int-abs
/
abs-07
int-abs
/
abs-16
int-abs
/
forward-le-05