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Definition df-ceil 12802
 Description: The ceiling (least integer greater than or equal to) function. Defined in ISO 80000-2:2009(E) operation 2-9.18 and the "NIST Digital Library of Mathematical Functions" , front introduction, "Common Notations and Definitions" section at http://dlmf.nist.gov/front/introduction#Sx4. See ceilval 12847 for its value, ceilge 12853 and ceilm1lt 12855 for its basic properties, and ceilcl 12851 for its closure. For example, (⌈‘(3 / 2)) = 2 while (⌈‘-(3 / 2)) = -1 (ex-ceil 27647). The symbol ⌈ is inspired by the gamma shaped left bracket of the usual notation. (Contributed by David A. Wheeler, 19-May-2015.)
Assertion
Ref Expression
df-ceil ⌈ = (𝑥 ∈ ℝ ↦ -(⌊‘-𝑥))

Detailed syntax breakdown of Definition df-ceil
StepHypRef Expression
1 cceil 12800 . 2 class
2 vx . . 3 setvar 𝑥
3 cr 10137 . . 3 class
42cv 1630 . . . . . 6 class 𝑥
54cneg 10469 . . . . 5 class -𝑥
6 cfl 12799 . . . . 5 class
75, 6cfv 6031 . . . 4 class (⌊‘-𝑥)
87cneg 10469 . . 3 class -(⌊‘-𝑥)
92, 3, 8cmpt 4863 . 2 class (𝑥 ∈ ℝ ↦ -(⌊‘-𝑥))
101, 9wceq 1631 1 wff ⌈ = (𝑥 ∈ ℝ ↦ -(⌊‘-𝑥))
 Colors of variables: wff setvar class This definition is referenced by:  ceilval  12847  dfceil2  12848
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