Description: The metric of a subcomplex Hilbert space augmented with betweenness. (Contributed by Thierry Arnoux, 25-Mar-2019)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ttgval.n | ||
ttgds.1 | |||
Assertion | ttgds |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ttgval.n | ||
2 | ttgds.1 | ||
3 | df-ds | ||
4 | 1nn0 | ||
5 | 2nn | ||
6 | 4 5 | decnncl | |
7 | 2nn0 | ||
8 | 6nn | ||
9 | 2lt6 | ||
10 | 4 7 8 9 | declt | |
11 | 1 3 6 10 | ttglem | |
12 | 2 11 | eqtri |