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Definition df-fzo 9101
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 8976, which includes  N. Not including the endpoint simplifies a number of formulae related to cardinality and splitting; contrast fzosplit 9134 with fzsplit 9016, 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 9100 . 2  class ..^
2 vm . . 3  setvar  m
3 vn . . 3  setvar  n
4 cz 8301 . . 3  class  ZZ
52cv 1258 . . . 4  class  m
63cv 1258 . . . . 5  class  n
7 c1 6947 . . . . 5  class  1
8 cmin 7244 . . . . 5  class  -
96, 7, 8co 5539 . . . 4  class  ( n  -  1 )
10 cfz 8975 . . . 4  class  ...
115, 9, 10co 5539 . . 3  class  ( m ... ( n  - 
1 ) )
122, 3, 4, 4, 11cmpt2 5541 . 2  class  ( m  e.  ZZ ,  n  e.  ZZ  |->  ( m ... ( n  -  1
) ) )
131, 12wceq 1259 1  wff ..^  =  ( m  e.  ZZ ,  n  e.  ZZ  |->  ( m ... ( n  - 
1 ) ) )
Colors of variables: wff set class
This definition is referenced by:  fzof  9102  elfzoel1  9103  elfzoel2  9104  fzoval  9106
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