Theorem flle

Description: A basic property of the floor (greatest integer) function. (Contributed by NM, 24-Feb-2005)

	Ref	Expression
Assertion	flle	$$⊢A\in ℝ\to ⌊A⌋\le A$$

Proof

Step	Hyp	Ref	Expression
1		fllelt	$$⊢A\in ℝ\to \left(⌊A⌋\le A\wedge A<⌊A⌋+1\right)$$
2	1	simpld	$$⊢A\in ℝ\to ⌊A⌋\le A$$