Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-fzo Structured version   Unicode version

Definition df-fzo 11167
 Description: Define a function generating sets of integers using a half-open range. Read ..^ as the integers from up to, but not including, ; contrast with df-fz 11075, which includes . 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 ..^
Distinct variable group:   ,

Detailed syntax breakdown of Definition df-fzo
StepHypRef Expression
1 cfzo 11166 . 2 ..^
2 vm . . 3
3 vn . . 3
4 cz 10313 . . 3
52cv 1652 . . . 4
63cv 1652 . . . . 5
7 c1 9022 . . . . 5
8 cmin 9322 . . . . 5
96, 7, 8co 6110 . . . 4
10 cfz 11074 . . . 4
115, 9, 10co 6110 . . 3
122, 3, 4, 4, 11cmpt2 6112 . 2
131, 12wceq 1653 1 ..^
 Colors of variables: wff set class This definition is referenced by:  fzof  11168  fzoval  11172
 Copyright terms: Public domain W3C validator