Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > df-reap | Unicode version |
Description: Define real apartness. Definition in Section 11.2.1 of [HoTT], p. (varies). Although #ℝ is an apartness relation on the reals (see df-ap 8501 for more discussion of apartness relations), for our purposes it is just a stepping stone to defining # which is an apartness relation on complex numbers. On the reals, #ℝ and # agree (apreap 8506). (Contributed by Jim Kingdon, 26-Jan-2020.) |
Ref | Expression |
---|---|
df-reap | #ℝ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | creap 8493 | . 2 #ℝ | |
2 | vx | . . . . . . 7 | |
3 | 2 | cv 1347 | . . . . . 6 |
4 | cr 7773 | . . . . . 6 | |
5 | 3, 4 | wcel 2141 | . . . . 5 |
6 | vy | . . . . . . 7 | |
7 | 6 | cv 1347 | . . . . . 6 |
8 | 7, 4 | wcel 2141 | . . . . 5 |
9 | 5, 8 | wa 103 | . . . 4 |
10 | clt 7954 | . . . . . 6 | |
11 | 3, 7, 10 | wbr 3989 | . . . . 5 |
12 | 7, 3, 10 | wbr 3989 | . . . . 5 |
13 | 11, 12 | wo 703 | . . . 4 |
14 | 9, 13 | wa 103 | . . 3 |
15 | 14, 2, 6 | copab 4049 | . 2 |
16 | 1, 15 | wceq 1348 | 1 #ℝ |
Colors of variables: wff set class |
This definition is referenced by: reapval 8495 |
Copyright terms: Public domain | W3C validator |