Description: Obsolete proof of tngip as of 31-Oct-2024. The inner product operation 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 ) |
|
| tngip.2 | |- ., = ( .i ` G ) |
||
| Assertion | tngipOLD | |- ( N e. V -> ., = ( .i ` T ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | tngbas.t | |- T = ( G toNrmGrp N ) |
|
| 2 | tngip.2 | |- ., = ( .i ` G ) |
|
| 3 | df-ip | |- .i = Slot 8 |
|
| 4 | 8nn | |- 8 e. NN |
|
| 5 | 8lt9 | |- 8 < 9 |
|
| 6 | 1 3 4 5 | tnglemOLD | |- ( N e. V -> ( .i ` G ) = ( .i ` T ) ) |
| 7 | 2 6 | eqtrid | |- ( N e. V -> ., = ( .i ` T ) ) |