Theorem fldivnn0

Description: The floor function of a division of a nonnegative integer by a positive integer is a nonnegative integer. (Contributed by Alexander van der Vekens, 14-Apr-2018)

	Ref	Expression
Assertion	fldivnn0	|- ( ( K e. NN0 /\ L e. NN ) -> ( |_ ` ( K / L ) ) e. NN0 )

Proof

Step	Hyp	Ref	Expression
1		nn0nndivcl	|- ( ( K e. NN0 /\ L e. NN ) -> ( K / L ) e. RR )
2		nn0ge0div	|- ( ( K e. NN0 /\ L e. NN ) -> 0 <_ ( K / L ) )
3		flge0nn0	|- ( ( ( K / L ) e. RR /\ 0 <_ ( K / L ) ) -> ( |_ ` ( K / L ) ) e. NN0 )
4	1 2 3	syl2anc	|- ( ( K e. NN0 /\ L e. NN ) -> ( |_ ` ( K / L ) ) e. NN0 )