Metamath Proof Explorer

Theorem uzssre2

Description: An upper set of integers is a subset of the Reals. (Contributed by Glauco Siliprandi, 23-Oct-2021)

Ref Expression
Hypothesis uzssre2.1 
|- Z = ( ZZ>= ` M )
Assertion uzssre2 
|- Z C_ RR

Proof

Step Hyp Ref Expression
1 uzssre2.1 
 |-  Z = ( ZZ>= ` M )
2 uzssz 
 |-  ( ZZ>= ` M ) C_ ZZ
3 zssre 
 |-  ZZ C_ RR
4 2 3 sstri 
 |-  ( ZZ>= ` M ) C_ RR
5 1 4 eqsstri 
 |-  Z C_ RR