Metamath Proof Explorer

Theorem oddp1div2z

Description: The result of dividing an odd number increased by 1 and then divided by 2 is an integer. (Contributed by AV, 15-Jun-2020)

Ref Expression
Assertion oddp1div2z 
|- ( Z e. Odd -> ( ( Z + 1 ) / 2 ) e. ZZ )

Proof

Step Hyp Ref Expression
1 isodd 
 |-  ( Z e. Odd <-> ( Z e. ZZ /\ ( ( Z + 1 ) / 2 ) e. ZZ ) )
2 1 simprbi 
 |-  ( Z e. Odd -> ( ( Z + 1 ) / 2 ) e. ZZ )