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