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 | |
||
ltord2.6 | |
||
Assertion | leord2 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ltord.1 | |
|
2 | ltord.2 | |
|
3 | ltord.3 | |
|
4 | ltord.4 | |
|
5 | ltord.5 | |
|
6 | ltord2.6 | |
|
7 | 1 | negeqd | |
8 | 2 | negeqd | |
9 | 3 | negeqd | |
10 | 5 | renegcld | |
11 | 5 | ralrimiva | |
12 | 1 | eleq1d | |
13 | 12 | rspccva | |
14 | 11 13 | sylan | |
15 | 14 | adantrl | |
16 | 5 | adantrr | |
17 | ltneg | |
|
18 | 15 16 17 | syl2anc | |
19 | 6 18 | sylibd | |
20 | 7 8 9 4 10 19 | leord1 | |
21 | 3 | eleq1d | |
22 | 21 | rspccva | |
23 | 11 22 | sylan | |
24 | 23 | adantrl | |
25 | 2 | eleq1d | |
26 | 25 | rspccva | |
27 | 11 26 | sylan | |
28 | 27 | adantrr | |
29 | leneg | |
|
30 | 24 28 29 | syl2anc | |
31 | 20 30 | bitr4d | |