Description: Hilbert space addition with the zero vector. (Contributed by NM, 7-Sep-2007) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | hladdid.1 | |- X = ( BaseSet ` U ) |
|
hladdid.2 | |- G = ( +v ` U ) |
||
hladdid.5 | |- Z = ( 0vec ` U ) |
||
Assertion | hladdid | |- ( ( U e. CHilOLD /\ A e. X ) -> ( A G Z ) = A ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hladdid.1 | |- X = ( BaseSet ` U ) |
|
2 | hladdid.2 | |- G = ( +v ` U ) |
|
3 | hladdid.5 | |- Z = ( 0vec ` U ) |
|
4 | hlnv | |- ( U e. CHilOLD -> U e. NrmCVec ) |
|
5 | 1 2 3 | nv0rid | |- ( ( U e. NrmCVec /\ A e. X ) -> ( A G Z ) = A ) |
6 | 4 5 | sylan | |- ( ( U e. CHilOLD /\ A e. X ) -> ( A G Z ) = A ) |