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Mirrors > Home > MPE Home > Th. List > df-zn | Structured version Visualization version Unicode version |
Description: Define the ring of integers . This is literally the quotient ring of by the ideal , but we augment it with a total order. (Contributed by Mario Carneiro, 14-Jun-2015.) (Revised by AV, 12-Jun-2019.) |
Ref | Expression |
---|---|
df-zn | ℤ/nℤ ℤring s ~QG RSpan sSet RHom ..^ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | czn 19851 | . 2 ℤ/nℤ | |
2 | vn | . . 3 | |
3 | cn0 11292 | . . 3 | |
4 | vz | . . . 4 | |
5 | zring 19818 | . . . 4 ℤring | |
6 | vs | . . . . 5 | |
7 | 4 | cv 1482 | . . . . . 6 |
8 | 2 | cv 1482 | . . . . . . . . 9 |
9 | 8 | csn 4177 | . . . . . . . 8 |
10 | crsp 19171 | . . . . . . . . 9 RSpan | |
11 | 7, 10 | cfv 5888 | . . . . . . . 8 RSpan |
12 | 9, 11 | cfv 5888 | . . . . . . 7 RSpan |
13 | cqg 17590 | . . . . . . 7 ~QG | |
14 | 7, 12, 13 | co 6650 | . . . . . 6 ~QG RSpan |
15 | cqus 16165 | . . . . . 6 s | |
16 | 7, 14, 15 | co 6650 | . . . . 5 s ~QG RSpan |
17 | 6 | cv 1482 | . . . . . 6 |
18 | cnx 15854 | . . . . . . . 8 | |
19 | cple 15948 | . . . . . . . 8 | |
20 | 18, 19 | cfv 5888 | . . . . . . 7 |
21 | vf | . . . . . . . 8 | |
22 | czrh 19848 | . . . . . . . . . 10 RHom | |
23 | 17, 22 | cfv 5888 | . . . . . . . . 9 RHom |
24 | cc0 9936 | . . . . . . . . . . 11 | |
25 | 8, 24 | wceq 1483 | . . . . . . . . . 10 |
26 | cz 11377 | . . . . . . . . . 10 | |
27 | cfzo 12465 | . . . . . . . . . . 11 ..^ | |
28 | 24, 8, 27 | co 6650 | . . . . . . . . . 10 ..^ |
29 | 25, 26, 28 | cif 4086 | . . . . . . . . 9 ..^ |
30 | 23, 29 | cres 5116 | . . . . . . . 8 RHom ..^ |
31 | 21 | cv 1482 | . . . . . . . . . 10 |
32 | cle 10075 | . . . . . . . . . 10 | |
33 | 31, 32 | ccom 5118 | . . . . . . . . 9 |
34 | 31 | ccnv 5113 | . . . . . . . . 9 |
35 | 33, 34 | ccom 5118 | . . . . . . . 8 |
36 | 21, 30, 35 | csb 3533 | . . . . . . 7 RHom ..^ |
37 | 20, 36 | cop 4183 | . . . . . 6 RHom ..^ |
38 | csts 15855 | . . . . . 6 sSet | |
39 | 17, 37, 38 | co 6650 | . . . . 5 sSet RHom ..^ |
40 | 6, 16, 39 | csb 3533 | . . . 4 s ~QG RSpan sSet RHom ..^ |
41 | 4, 5, 40 | csb 3533 | . . 3 ℤring s ~QG RSpan sSet RHom ..^ |
42 | 2, 3, 41 | cmpt 4729 | . 2 ℤring s ~QG RSpan sSet RHom ..^ |
43 | 1, 42 | wceq 1483 | 1 ℤ/nℤ ℤring s ~QG RSpan sSet RHom ..^ |
Colors of variables: wff setvar class |
This definition is referenced by: znval 19883 |
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