Definition df-fzo 9000

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 8875, which includes N. Not including the endpoint simplifies a number of formulae related to cardinality and splitting; contrast fzosplit 9033 with fzsplit 8915, 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 8999	. 2 class ..^
2		vm	. . 3 setvar m
3		vn	. . 3 setvar n
4		cz 8245	. . 3 class ZZ
5	2	cv 1242	. . . 4 class m
6	3	cv 1242	. . . . 5 class n
7		c1 6890	. . . . 5 class 1
8		cmin 7182	. . . . 5 class -
9	6, 7, 8	co 5512	. . . 4 class ( n - 1 )
10		cfz 8874	. . . 4 class ...
11	5, 9, 10	co 5512	. . 3 class ( m ... ( n - 1 ) )
12	2, 3, 4, 4, 11	cmpt2 5514	. 2 class ( m e. ZZ , n e. ZZ |-> ( m ... ( n - 1 ) ) )
13	1, 12	wceq 1243	1 wff ..^ = ( m e. ZZ , n e. ZZ |-> ( m ... ( n - 1 ) ) )

This definition is referenced by:  fzof  9001  elfzoel1  9002  elfzoel2  9003  fzoval  9005