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for | Def For{T,op,id} x as. f(x) == reduce(op;id;map(x:T. f(x);as)) |
| | Thm* A,B,C:Type, f:(BCC), k:C, as:A List, g:(AB).
Thm* (For{A,f,k} x as. g(x)) C |
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tlambda | Def (x:T. b(x))(x) == b(x) |
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map | Def map(f;as) == Case of as; nil nil ; a.as' f(a).map(f;as') (recursive) |
| | Thm* A,B:Type, f:(AB), l:A List. map(f;l) B List |
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reduce | Def reduce(f;k;as) == Case of as; nil k ; a.as' f(a,reduce(f;k;as'))
Def (recursive) |
| | Thm* A,B:Type, f:(ABB), k:B, as:A List. reduce(f;k;as) B |