Metamath Proof Explorer
		
		
		
		Description:  An upper set of integers is a subset of the complex numbers.
       (Contributed by Glauco Siliprandi, 5-Feb-2022)
		
			
				
					 | 
					 | 
					Ref | 
					Expression | 
				
					
						 | 
						Hypothesis | 
						uzsscn2.1 | 
						|- Z = ( ZZ>= ` M )  | 
					
				
					 | 
					Assertion | 
					uzsscn2 | 
					|- Z C_ CC  | 
				
			
		
		
			
				Proof
				
					
						| Step | 
						Hyp | 
						Ref | 
						Expression | 
					
						
							| 1 | 
							
								
							 | 
							uzsscn2.1 | 
							 |-  Z = ( ZZ>= ` M )  | 
						
						
							| 2 | 
							
								
							 | 
							uzsscn | 
							 |-  ( ZZ>= ` M ) C_ CC  | 
						
						
							| 3 | 
							
								1 2
							 | 
							eqsstri | 
							 |-  Z C_ CC  |