Theorem ceilged

Description: The ceiling of a real number is greater than or equal to that number. (Contributed by Glauco Siliprandi, 2-Jan-2022)

	Ref	Expression
Hypothesis	ceilged.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
Assertion	ceilged	⊢ ( 𝜑 → 𝐴 ≤ ( ⌈ ‘ 𝐴 ) )

Proof

Step	Hyp	Ref	Expression
1		ceilged.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
2		ceilge	⊢ ( 𝐴 ∈ ℝ → 𝐴 ≤ ( ⌈ ‘ 𝐴 ) )
3	1 2	syl	⊢ ( 𝜑 → 𝐴 ≤ ( ⌈ ‘ 𝐴 ) )