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Metamath Proof Explorer
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 ) |