Definition df-fzo 10099

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 9966, which includes N. Not including the endpoint simplifies a number of formulas related to cardinality and splitting; contrast fzosplit 10133 with fzsplit 10007, 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 10098	. 2 class ..^
2		vm	. . 3 setvar m
3		vn	. . 3 setvar n
4		cz 9212	. . 3 class ZZ
5	2	cv 1347	. . . 4 class m
6	3	cv 1347	. . . . 5 class n
7		c1 7775	. . . . 5 class 1
8		cmin 8090	. . . . 5 class -
9	6, 7, 8	co 5853	. . . 4 class ( n - 1 )
10		cfz 9965	. . . 4 class ...
11	5, 9, 10	co 5853	. . 3 class ( m ... ( n - 1 ) )
12	2, 3, 4, 4, 11	cmpo 5855	. 2 class ( m e. ZZ , n e. ZZ |-> ( m ... ( n - 1 ) ) )
13	1, 12	wceq 1348	1 wff ..^ = ( m e. ZZ , n e. ZZ |-> ( m ... ( n - 1 ) ) )

This definition is referenced by:  fzof  10100  elfzoel1  10101  elfzoel2  10102  fzoval  10104