| Some definitions of interest. |
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swap_adjacent | Def swap adjacent[P(x;y)](L1,L2)
Def == i: (||L1||-1). P(L1[i];L1[(i+1)]) & L2 = swap(L1;i;i+1) A List |
| | Thm* A:Type, P:(A![](FONT/dash.png) A![](FONT/dash.png) Prop). swap adjacent[P(x,y)] (A List)![](FONT/dash.png) (A List)![](FONT/dash.png) Prop |
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int_seg | Def {i..j } == {k: | i k < j } |
| | Thm* m,n: . {m..n } Type |
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swap | Def swap(L;i;j) == (L o (i, j)) |
| | Thm* T:Type, L:T List, i,j: ||L||. swap(L;i;j) T List |
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length | Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive) |
| | Thm* A:Type, l:A List. ||l|| ![](FONT/int.png) |
| | Thm* ||nil|| ![](FONT/int.png) |
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not | Def A == A ![](FONT/eq.png) False |
| | Thm* A:Prop. ( A) Prop |
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select | Def l[i] == hd(nth_tl(i;l)) |
| | Thm* A:Type, l:A List, n: . 0 n ![](FONT/eq.png) n<||l|| ![](FONT/eq.png) l[n] A |
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sym | Def Sym x,y:T. E(x;y) == a,b:T. E(a;b) ![](FONT/eq.png) E(b;a) |
| | Thm* T:Type, E:(T![](FONT/dash.png) T![](FONT/dash.png) Prop). (Sym x,y:T. E(x,y)) Prop |