Description: The infimum of the set of positive integers is one. (Contributed by NM, 16-Jun-2005) (Revised by AV, 5-Sep-2020)
Ref | Expression | ||
---|---|---|---|
Assertion | nninf | |- inf ( NN , RR , < ) = 1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnuz | |- NN = ( ZZ>= ` 1 ) |
|
2 | 1 | infeq1i | |- inf ( NN , RR , < ) = inf ( ( ZZ>= ` 1 ) , RR , < ) |
3 | 1z | |- 1 e. ZZ |
|
4 | 3 | uzinfi | |- inf ( ( ZZ>= ` 1 ) , RR , < ) = 1 |
5 | 2 4 | eqtri | |- inf ( NN , RR , < ) = 1 |