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Mirrors > Home > ILE Home > Th. List > df-iltp | Unicode version |
Description: Define ordering on
positive reals. We define
if there is a
positive fraction which is an element of the upper cut of
and the lower cut of . From the definition of < in Section 11.2.1
of [HoTT], p. (varies).
This is a "temporary" set used in the construction of complex numbers, and is intended to be used only by the construction. (Contributed by Jim Kingdon, 29-Sep-2019.) |
Ref | Expression |
---|---|
df-iltp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cltp 7215 | . 2 | |
2 | vx | . . . . . . 7 | |
3 | 2 | cv 1334 | . . . . . 6 |
4 | cnp 7211 | . . . . . 6 | |
5 | 3, 4 | wcel 2128 | . . . . 5 |
6 | vy | . . . . . . 7 | |
7 | 6 | cv 1334 | . . . . . 6 |
8 | 7, 4 | wcel 2128 | . . . . 5 |
9 | 5, 8 | wa 103 | . . . 4 |
10 | vq | . . . . . . . 8 | |
11 | 10 | cv 1334 | . . . . . . 7 |
12 | c2nd 6087 | . . . . . . . 8 | |
13 | 3, 12 | cfv 5170 | . . . . . . 7 |
14 | 11, 13 | wcel 2128 | . . . . . 6 |
15 | c1st 6086 | . . . . . . . 8 | |
16 | 7, 15 | cfv 5170 | . . . . . . 7 |
17 | 11, 16 | wcel 2128 | . . . . . 6 |
18 | 14, 17 | wa 103 | . . . . 5 |
19 | cnq 7200 | . . . . 5 | |
20 | 18, 10, 19 | wrex 2436 | . . . 4 |
21 | 9, 20 | wa 103 | . . 3 |
22 | 21, 2, 6 | copab 4024 | . 2 |
23 | 1, 22 | wceq 1335 | 1 |
Colors of variables: wff set class |
This definition is referenced by: ltrelpr 7425 ltdfpr 7426 |
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