Metamath Proof Explorer

Theorem zefldiv2

Description: The floor of an even integer divided by 2 is equal to the integer divided by 2. (Contributed by AV, 7-Jun-2020)

Ref Expression
Assertion zefldiv2 
|- ( ( N e. ZZ /\ ( N / 2 ) e. ZZ ) -> ( |_ ` ( N / 2 ) ) = ( N / 2 ) )

Proof

Step Hyp Ref Expression
1 flid 
 |-  ( ( N / 2 ) e. ZZ -> ( |_ ` ( N / 2 ) ) = ( N / 2 ) )
2 1 adantl 
 |-  ( ( N e. ZZ /\ ( N / 2 ) e. ZZ ) -> ( |_ ` ( N / 2 ) ) = ( N / 2 ) )