Metamath Proof Explorer
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 ) ) |