Description: The addition operation of a subcomplex Hilbert space augmented with betweenness. (Contributed by Thierry Arnoux, 25-Mar-2019)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | ttgval.n | |- G = ( toTG ` H ) |
|
| ttgplusg.1 | |- .+ = ( +g ` H ) |
||
| Assertion | ttgplusg | |- .+ = ( +g ` G ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ttgval.n | |- G = ( toTG ` H ) |
|
| 2 | ttgplusg.1 | |- .+ = ( +g ` H ) |
|
| 3 | df-plusg | |- +g = Slot 2 |
|
| 4 | 2nn | |- 2 e. NN |
|
| 5 | 1nn | |- 1 e. NN |
|
| 6 | 6nn0 | |- 6 e. NN0 |
|
| 7 | 2nn0 | |- 2 e. NN0 |
|
| 8 | 2lt10 | |- 2 < ; 1 0 |
|
| 9 | 5 6 7 8 | declti | |- 2 < ; 1 6 |
| 10 | 1 3 4 9 | ttglem | |- ( +g ` H ) = ( +g ` G ) |
| 11 | 2 10 | eqtri | |- .+ = ( +g ` G ) |