| Some definitions of interest. |
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gt | Def i>j == j<i |
| | Thm* i,j: . (i>j) Prop |
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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:(A B). 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: | 0 i } |
| | Thm* Type |
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le | Def A B == B<A |
| | Thm* i,j: . (i j) Prop |
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length | Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive) |
| | Thm* A:Type, l:A List. ||l||  |
| | Thm* ||nil||  |
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select | Def l[i] == hd(nth_tl(i;l)) |
| | Thm* A:Type, l:A List, n: . 0 n  n<||l||  l[n] A |
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sum | Def sum(f(x) | x < k) == primrec(k;0; x,n. n+f(x)) |
| | Thm* n: , f:( n  ). sum(f(x) | x < n)  |