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