| Some definitions of interest. |
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firstn | Def firstn(n;as)
Def == Case of as; nil nil ; a.as' if 0< n a.firstn(n-1;as') else nil fi
Def (recursive) |
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| Thm* A:Type, as:A List, n: . firstn(n;as) A List |
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int_iseg | Def {i...j} == {k: | i k & k j } |
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| Thm* i,j: . {i...j} Type |
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int_seg | Def {i..j } == {k: | i k < j } |
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| Thm* m,n: . {m..n } Type |
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nat | Def == {i: | 0 i } |
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| Thm* Type |
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le | Def A B == B<A |
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| Thm* i,j: . (i j) Prop |
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length | Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive) |
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| Thm* A:Type, l:A List. ||l||  |
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| Thm* ||nil||  |
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select | Def l[i] == hd(nth_tl(i;l)) |
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| Thm* A:Type, l:A List, n: . 0 n  n<||l||  l[n] A |