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Theorem add-def-02
0 < j1, 0 < j2 ⊦ rational(i1, j1) + rational(i2, j2) = rational(i1 * j2 + j1 * i2, j1 * j2)
Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
add-def-03
,
Used by units in proved state:
Proof exists?: Yes
View
the proof
Infos about the proof
Proved?: Yes
Interactions: 20
Proof steps: 31
Used lemmas:
add-zero
,
add-comm
,
zero-def
,
zero-num
,
factor-rat-02
,
factor-rat-01
,
factor-rat-03
,
add-def-01
,
Used spec theorems:
int-mult
/
commutativity
int-gcd
/
gcd-one
int-mult
/
associativity
int-mult
/
zero-eq
Used simplifier rules:
nat-basic2
/
c
nat-basic2
/
a
int-mult
/
le-same-05
int-abs
/
abs
int-mult
/
abs-eqall
intnat
/
labs
nat-basic2
/
l
int-abs
/
lels-02
int-basic1
/
ls-01
int-mult
/
zero-eq
int-basic2
/
add-zero
int-gcd
/
gcd-zero-04
int-mult
/
Mult-zero
int-mult
/
zero-gr
int-basic2
/
add-a
int-mult
/
associativity
int-mult
/
dist-rmerge
int-basic1
/
forward-pos
int-gcd
/
divides
int-abs
/
gr-def
int-abs
/
forward-le-05
int-abs
/
lels-03
int-abs
/
lels
int-mult
/
commutativity
int-basic2
/
add-c