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 ∈ Odd → ( ( 𝑍 + 1 ) / 2 ) ∈ ℤ )

Proof

Step	Hyp	Ref	Expression
1		isodd	⊢ ( 𝑍 ∈ Odd ↔ ( 𝑍 ∈ ℤ ∧ ( ( 𝑍 + 1 ) / 2 ) ∈ ℤ ) )
2	1	simprbi	⊢ ( 𝑍 ∈ Odd → ( ( 𝑍 + 1 ) / 2 ) ∈ ℤ )