Metamath Proof Explorer


Theorem fldivnn0le

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

Ref Expression
Assertion fldivnn0le K0LKLKL

Proof

Step Hyp Ref Expression
1 nn0re K0K
2 nnrp LL+
3 fldivle KL+KLKL
4 1 2 3 syl2an K0LKLKL