Theorem ceilge

Description: The ceiling of a real number is greater than or equal to that number. (Contributed by AV, 30-Nov-2018)

	Ref	Expression
Assertion	ceilge	$$⊢A\in ℝ\to A\le ⌈A⌉$$

Proof

Step	Hyp	Ref	Expression
1		ceige	$$⊢A\in ℝ\to A\le -⌊-A⌋$$
2		ceilval	$$⊢A\in ℝ\to ⌈A⌉=-⌊-A⌋$$
3	1 2	breqtrrd	$$⊢A\in ℝ\to A\le ⌈A⌉$$