Database
SUPPLEMENTARY MATERIAL (USERS' MATHBOXES)
Mathbox for Andrew Salmon
Geometry
df-addr
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df-subr
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Definition
df-addr
Description:
Define the operation of vector addition.
(Contributed by
Andrew Salmon
, 27-Jan-2012)
Ref
Expression
Assertion
df-addr
⊢
+
r
=
x
∈
V
,
y
∈
V
⟼
v
∈
ℝ
⟼
x
⁡
v
+
y
⁡
v
Detailed syntax breakdown
Step
Hyp
Ref
Expression
0
cplusr
class
+
r
1
vx
setvar
x
2
cvv
class
V
3
vy
setvar
y
4
vv
setvar
v
5
cr
class
ℝ
6
1
cv
setvar
x
7
4
cv
setvar
v
8
7
6
cfv
class
x
⁡
v
9
caddc
class
+
10
3
cv
setvar
y
11
7
10
cfv
class
y
⁡
v
12
8
11
9
co
class
x
⁡
v
+
y
⁡
v
13
4
5
12
cmpt
class
v
∈
ℝ
⟼
x
⁡
v
+
y
⁡
v
14
1
3
2
2
13
cmpo
class
x
∈
V
,
y
∈
V
⟼
v
∈
ℝ
⟼
x
⁡
v
+
y
⁡
v
15
0
14
wceq
wff
+
r
=
x
∈
V
,
y
∈
V
⟼
v
∈
ℝ
⟼
x
⁡
v
+
y
⁡
v