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Theorem equality-pos
i * j0 = i0 * j, 0 < j, 0 < j0, 0 < i, 0 < i0 ⊦ rational(i, j) = rational(i0, j0)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
equality-02
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 15
Proof steps: 22
Used lemmas:
denominator-pos
,
num-pos
,
Equality
,
Used spec theorems:
int-gcd
/
gcd-div-eq
int-gcd
/
gcd-div-mult-shift
int-gcd
/
gcd-mult-pos
int-div
/
div-mult
int-mult
/
commutativity
int-gcd
/
gcd-mult-pos-01
Used simplifier rules:
int-gcd
/
gcd-zero-zero
int-div
/
div-mult-03
int-gcd
/
gcd-mult
int-abs
/
lels
int-abs
/
lels-02
int-basic1
/
ls-01
int-abs
/
lels-01
int-gcd
/
gcd-com
int-mult
/
zero-eq
int-abs
/
abs-16
int-mult
/
Mult-zero
int-mult
/
associativity
int-mult
/
commutativity
int-mult
/
zero-neq-01
int-abs
/
forward-le-05