Description: A member of a set of extended reals is greater than or equal to the set's infimum. (Contributed by Mario Carneiro, 16-Mar-2014) (Revised by AV, 5-Sep-2020)
Ref | Expression | ||
---|---|---|---|
Assertion | infxrlb | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | infxrcl | |
|
2 | 1 | adantr | |
3 | ssel2 | |
|
4 | xrltso | |
|
5 | 4 | a1i | |
6 | xrinfmss | |
|
7 | 5 6 | inflb | |
8 | 7 | imp | |
9 | 2 3 8 | xrnltled | |