MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-fzo Structured version   Visualization version   GIF version

Definition df-fzo 13038
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 12895, which includes 𝑁. Not including the endpoint simplifies a number of formulas related to cardinality and splitting; contrast fzosplit 13074 with fzsplit 12937, 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 13037 . 2 class ..^
2 vm . . 3 setvar 𝑚
3 vn . . 3 setvar 𝑛
4 cz 11978 . . 3 class
52cv 1537 . . . 4 class 𝑚
63cv 1537 . . . . 5 class 𝑛
7 c1 10536 . . . . 5 class 1
8 cmin 10868 . . . . 5 class
96, 7, 8co 7149 . . . 4 class (𝑛 − 1)
10 cfz 12894 . . . 4 class ...
115, 9, 10co 7149 . . 3 class (𝑚...(𝑛 − 1))
122, 3, 4, 4, 11cmpo 7151 . 2 class (𝑚 ∈ ℤ, 𝑛 ∈ ℤ ↦ (𝑚...(𝑛 − 1)))
131, 12wceq 1538 1 wff ..^ = (𝑚 ∈ ℤ, 𝑛 ∈ ℤ ↦ (𝑚...(𝑛 − 1)))
Colors of variables: wff setvar class
This definition is referenced by:  fzof  13039  fzoval  13043
  Copyright terms: Public domain W3C validator