Description: Obsolete proof of tngplusg as of 31-Oct-2024. The group addition of a structure augmented with a norm. (Contributed by Mario Carneiro, 2-Oct-2015) (New usage is discouraged.) (Proof modification is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | tngbas.t | |- T = ( G toNrmGrp N ) |
|
| tngplusg.2 | |- .+ = ( +g ` G ) |
||
| Assertion | tngplusgOLD | |- ( 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 | tnglemOLD | |- ( N e. V -> ( +g ` G ) = ( +g ` T ) ) |
| 7 | 2 6 | eqtrid | |- ( N e. V -> .+ = ( +g ` T ) ) |