ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  df-fzo GIF version

Definition df-fzo 9230
Description: Define a function generating sets of integers using a half-open range. Read (𝑀..^𝑁) as the integers from 𝑀 up to, but not including, 𝑁; contrast with (𝑀...𝑁) df-fz 9106, which includes 𝑁. Not including the endpoint simplifies a number of formulae related to cardinality and splitting; contrast fzosplit 9263 with fzsplit 9146, for instance. (Contributed by Stefan O'Rear, 14-Aug-2015.)
Assertion
Ref Expression
df-fzo ..^ = (𝑚 ∈ ℤ, 𝑛 ∈ ℤ ↦ (𝑚...(𝑛 − 1)))
Distinct variable group:   𝑚,𝑛

Detailed syntax breakdown of Definition df-fzo
StepHypRef Expression
1 cfzo 9229 . 2 class ..^
2 vm . . 3 setvar 𝑚
3 vn . . 3 setvar 𝑛
4 cz 8432 . . 3 class
52cv 1284 . . . 4 class 𝑚
63cv 1284 . . . . 5 class 𝑛
7 c1 7044 . . . . 5 class 1
8 cmin 7346 . . . . 5 class
96, 7, 8co 5543 . . . 4 class (𝑛 − 1)
10 cfz 9105 . . . 4 class ...
115, 9, 10co 5543 . . 3 class (𝑚...(𝑛 − 1))
122, 3, 4, 4, 11cmpt2 5545 . 2 class (𝑚 ∈ ℤ, 𝑛 ∈ ℤ ↦ (𝑚...(𝑛 − 1)))
131, 12wceq 1285 1 wff ..^ = (𝑚 ∈ ℤ, 𝑛 ∈ ℤ ↦ (𝑚...(𝑛 − 1)))
Colors of variables: wff set class
This definition is referenced by:  fzof  9231  elfzoel1  9232  elfzoel2  9233  fzoval  9235
  Copyright terms: Public domain W3C validator