| Some definitions of interest. |
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increasing | Def increasing(f;k) == i: (k-1). f(i)<f(i+1) |
| | Thm* k: , f:( k  ). increasing(f;k) Prop |
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int_seg | Def {i..j } == {k: | i k < j } |
| | Thm* m,n: . {m..n } Type |
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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 |