Description: The scalar ring of a structure augmented with a norm. (Contributed by Mario Carneiro, 2-Oct-2015)
Ref | Expression | ||
---|---|---|---|
Hypotheses | tngbas.t | |- T = ( G toNrmGrp N ) |
|
tngsca.2 | |- F = ( Scalar ` G ) |
||
Assertion | tngsca | |- ( N e. V -> F = ( Scalar ` T ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tngbas.t | |- T = ( G toNrmGrp N ) |
|
2 | tngsca.2 | |- F = ( Scalar ` G ) |
|
3 | df-sca | |- Scalar = Slot 5 |
|
4 | 5nn | |- 5 e. NN |
|
5 | 5lt9 | |- 5 < 9 |
|
6 | 1 3 4 5 | tnglem | |- ( N e. V -> ( Scalar ` G ) = ( Scalar ` T ) ) |
7 | 2 6 | syl5eq | |- ( N e. V -> F = ( Scalar ` T ) ) |