| Some definitions of interest. |
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compose_iter | Def f{i}(x) == if i=0 x else f(f{i-1}(x)) fi (recursive) |
| | Thm* f:(AA), i:. f{i} AA |
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identity | Def Id(x) == x |
| | Thm* A:Type. Id AA |
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injection_type | Def A inj B == {f:(AB)| Inj(A; B; f) } |
| | Thm* A,B:Type. A inj B Type |
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inject | Def Inj(A; B; f) == a1,a2:A. f(a1) = f(a2) B a1 = a2 |
| | Thm* A,B:Type, f:(AB). Inj(A; B; f) Prop |
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int_seg | Def {i..j} == {k:| i k < j } |
| | Thm* m,n:. {m..n} Type |
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nat | Def == {i:| 0i } |
| | Thm* Type |
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nat_plus | Def == {i:| 0<i } |
| | Thm* Type |