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Definition df-fzo 11167
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 11075, which includes  N. Not including the endpoint simplifies a number of formulae related to cardinality and splitting; contrast fzosplit 11197 with fzsplit 11108, 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
StepHypRef Expression
1 cfzo 11166 . 2  class ..^
2 vm . . 3  set  m
3 vn . . 3  set  n
4 cz 10313 . . 3  class  ZZ
52cv 1652 . . . 4  class  m
63cv 1652 . . . . 5  class  n
7 c1 9022 . . . . 5  class  1
8 cmin 9322 . . . . 5  class  -
96, 7, 8co 6110 . . . 4  class  ( n  -  1 )
10 cfz 11074 . . . 4  class  ...
115, 9, 10co 6110 . . 3  class  ( m ... ( n  - 
1 ) )
122, 3, 4, 4, 11cmpt2 6112 . 2  class  ( m  e.  ZZ ,  n  e.  ZZ  |->  ( m ... ( n  -  1
) ) )
131, 12wceq 1653 1  wff ..^  =  ( m  e.  ZZ ,  n  e.  ZZ  |->  ( m ... ( n  - 
1 ) ) )
Colors of variables: wff set class
This definition is referenced by:  fzof  11168  fzoval  11172
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