Description: Two different elements of a half-open range are not congruent mod its length. (Contributed by Stefan O'Rear, 6-Sep-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | fzocongeq | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elfzoel2 | |
|
2 | elfzoel1 | |
|
3 | 1 2 | zsubcld | |
4 | elfzoelz | |
|
5 | elfzoelz | |
|
6 | zsubcl | |
|
7 | 4 5 6 | syl2an | |
8 | dvdsabsb | |
|
9 | 3 7 8 | syl2an2 | |
10 | fzomaxdif | |
|
11 | fzo0dvdseq | |
|
12 | 10 11 | syl | |
13 | 9 12 | bitrd | |
14 | 4 | zcnd | |
15 | 5 | zcnd | |
16 | subcl | |
|
17 | 14 15 16 | syl2an | |
18 | 17 | abs00ad | |
19 | subeq0 | |
|
20 | 14 15 19 | syl2an | |
21 | 18 20 | bitrd | |
22 | 13 21 | bitrd | |