Description: Infer an ordering relation from a proof in only one direction. (Contributed by Mario Carneiro, 14-Jun-2014)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ltord.1 | |
|
ltord.2 | |
||
ltord.3 | |
||
ltord.4 | |
||
ltord.5 | |
||
ltord.6 | |
||
Assertion | leord1 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ltord.1 | |
|
2 | ltord.2 | |
|
3 | ltord.3 | |
|
4 | ltord.4 | |
|
5 | ltord.5 | |
|
6 | ltord.6 | |
|
7 | 1 3 2 4 5 6 | ltord1 | |
8 | 7 | ancom2s | |
9 | 8 | notbid | |
10 | 4 | sseli | |
11 | 4 | sseli | |
12 | lenlt | |
|
13 | 10 11 12 | syl2an | |
14 | 13 | adantl | |
15 | 5 | ralrimiva | |
16 | 2 | eleq1d | |
17 | 16 | rspccva | |
18 | 15 17 | sylan | |
19 | 18 | adantrr | |
20 | 3 | eleq1d | |
21 | 20 | rspccva | |
22 | 15 21 | sylan | |
23 | 22 | adantrl | |
24 | 19 23 | lenltd | |
25 | 9 14 24 | 3bitr4d | |