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