Definition df-fzo 10140

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 10007, which includes N. Not including the endpoint simplifies a number of formulas related to cardinality and splitting; contrast fzosplit 10174 with fzsplit 10048, for instance. (Contributed by Stefan O'Rear, 14-Aug-2015.)

Assertion

Ref	Expression
df-fzo	|- ..^ = ( m e. ZZ , n e. ZZ |-> ( m ... ( n - 1 ) ) )

Distinct variable group:   m, n

Detailed syntax breakdown of Definition df-fzo

Step	Hyp	Ref	Expression
1		cfzo 10139	. 2 class ..^
2		vm	. . 3 setvar m
3		vn	. . 3 setvar n
4		cz 9251	. . 3 class ZZ
5	2	cv 1352	. . . 4 class m
6	3	cv 1352	. . . . 5 class n
7		c1 7811	. . . . 5 class 1
8		cmin 8126	. . . . 5 class -
9	6, 7, 8	co 5874	. . . 4 class ( n - 1 )
10		cfz 10006	. . . 4 class ...
11	5, 9, 10	co 5874	. . 3 class ( m ... ( n - 1 ) )
12	2, 3, 4, 4, 11	cmpo 5876	. 2 class ( m e. ZZ , n e. ZZ |-> ( m ... ( n - 1 ) ) )
13	1, 12	wceq 1353	1 wff ..^ = ( m e. ZZ , n e. ZZ |-> ( m ... ( n - 1 ) ) )

This definition is referenced by:  fzof  10141  elfzoel1  10142  elfzoel2  10143  fzoval  10145