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Theorem div-pos-def
⊦ 0 < i ∧ 0 < i0 ∧ 0 < j ∧ 0 < j0 → rational(i, j) / rational(i0, j0) = rational(i * j0, j * i0)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
div-def-01
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 14
Proof steps: 28
Used lemmas:
equality-def
,
denominator-zero
,
denominator-pos
,
num-pos
,
div-def
,
Used spec theorems:
int-mult
/
zero-le
int-gcd
/
gcd-div-mult-shift
int-div
/
div-div-pos
int-gcd
/
div-mult-shift
int-gcd
/
divides-mult-02
Used simplifier rules:
int-gcd
/
gcd-div1
int-mult
/
zero-eq
int-mult
/
zero-ge
int-abs
/
lels-01
int-gcd
/
gcd-less-eq-zero
int-gcd
/
gcd-divides
int-gcd
/
gcd-zero-zero
int-gcd
/
div-gcd-not-neg
int-abs
/
forward-le-04
int-abs
/
forward-lels
int-basic1
/
ls-01
int-abs
/
lels-02
int-mult
/
zero-gr
int-abs
/
lels
int-mult
/
one
int-mult
/
associativity
int-mult
/
commutativity
int-gcd
/
gcd-zero-04
int-abs
/
abs-16
int-gcd
/
gcd-com
int-mult
/
Mult-zero
int-abs
/
forward-le-05