Description: An upper bound to the distance of two elements in a closed interval. (Contributed by Glauco Siliprandi, 11-Dec-2019)
Ref | Expression | ||
---|---|---|---|
Hypotheses | iccsuble.1 | |
|
iccsuble.2 | |
||
iccsuble.3 | |
||
iccsuble.4 | |
||
Assertion | iccsuble | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iccsuble.1 | |
|
2 | iccsuble.2 | |
|
3 | iccsuble.3 | |
|
4 | iccsuble.4 | |
|
5 | eliccre | |
|
6 | 1 2 3 5 | syl3anc | |
7 | eliccre | |
|
8 | 1 2 4 7 | syl3anc | |
9 | elicc2 | |
|
10 | 1 2 9 | syl2anc | |
11 | 3 10 | mpbid | |
12 | 11 | simp3d | |
13 | elicc2 | |
|
14 | 1 2 13 | syl2anc | |
15 | 4 14 | mpbid | |
16 | 15 | simp2d | |
17 | 6 1 2 8 12 16 | le2subd | |