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Definition df-fzo 8750
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 8625, which includes 𝑁. Not including the endpoint simplifies a number of formulae related to cardinality and splitting; contrast fzosplit 8783 with fzsplit 8665, 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 8749 . 2 class ..^
2 vm . . 3 setvar 𝑚
3 vn . . 3 setvar 𝑛
4 cz 8001 . . 3 class
52cv 1241 . . . 4 class 𝑚
63cv 1241 . . . . 5 class 𝑛
7 c1 6692 . . . . 5 class 1
8 cmin 6959 . . . . 5 class
96, 7, 8co 5455 . . . 4 class (𝑛 − 1)
10 cfz 8624 . . . 4 class ...
115, 9, 10co 5455 . . 3 class (𝑚...(𝑛 − 1))
122, 3, 4, 4, 11cmpt2 5457 . 2 class (𝑚 ℤ, 𝑛 ℤ ↦ (𝑚...(𝑛 − 1)))
131, 12wceq 1242 1 wff ..^ = (𝑚 ℤ, 𝑛 ℤ ↦ (𝑚...(𝑛 − 1)))
Colors of variables: wff set class
This definition is referenced by:  fzof  8751  elfzoel1  8752  elfzoel2  8753  fzoval  8755
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