| Some definitions of interest. |
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iff | Def P ![](FONT/if_big.png) Q == (P ![](FONT/eq.png) Q) & (P ![](FONT/if_big.png) Q) |
| | Thm* A,B:Prop. (A ![](FONT/if_big.png) B) Prop |
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l_member | Def (x l) == i: . i<||l|| & x = l[i] T |
| | Thm* T:Type, x:T, l:T List. (x l) Prop |
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no_repeats | Def no_repeats(T;l) == i,j: . i<||l|| ![](FONT/eq.png) j<||l|| ![](FONT/eq.png) i = j ![](FONT/eq.png) l[i] = l[j] T |
| | Thm* T:Type, l:T List. no_repeats(T;l) 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|| ![](FONT/int.png) |
| | Thm* ||nil|| ![](FONT/int.png) |
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nat | Def == {i: | 0 i } |
| | Thm* Type |
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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 |