Description: Mapping for Hilbert space inner product. (Contributed by NM, 19-Nov-2007) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | hlipf.1 | |- X = ( BaseSet ` U ) |
|
hlipf.7 | |- P = ( .iOLD ` U ) |
||
Assertion | hlipf | |- ( U e. CHilOLD -> P : ( X X. X ) --> CC ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hlipf.1 | |- X = ( BaseSet ` U ) |
|
2 | hlipf.7 | |- P = ( .iOLD ` U ) |
|
3 | hlnv | |- ( U e. CHilOLD -> U e. NrmCVec ) |
|
4 | 1 2 | ipf | |- ( U e. NrmCVec -> P : ( X X. X ) --> CC ) |
5 | 3 4 | syl | |- ( U e. CHilOLD -> P : ( X X. X ) --> CC ) |