Description: The least upper bound property of subgroup sum. (Contributed by NM, 6-Feb-2014) (Revised by Mario Carneiro, 21-Jun-2014)
Ref | Expression | ||
---|---|---|---|
Hypothesis | lsmub1.p | |
|
Assertion | lsmlub | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | lsmub1.p | |
|
2 | simp3 | |
|
3 | 1 | lsmless12 | |
4 | 3 | ex | |
5 | 2 2 4 | syl2anc | |
6 | 1 | lsmidm | |
7 | 6 | 3ad2ant3 | |
8 | 7 | sseq2d | |
9 | 5 8 | sylibd | |
10 | 1 | lsmub1 | |
11 | 10 | 3adant3 | |
12 | sstr2 | |
|
13 | 11 12 | syl | |
14 | 1 | lsmub2 | |
15 | 14 | 3adant3 | |
16 | sstr2 | |
|
17 | 15 16 | syl | |
18 | 13 17 | jcad | |
19 | 9 18 | impbid | |