| Who Cites col list prod? |
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col_list_prod | Def col_list_prod(l)(x) == ||x|| = ||l|| & ( i: . i < ||x|| ![](FONT/eq.png) x[i] l[i]) |
| | Thm* T:Type, l:Collection(T) List. col_list_prod(l) Collection(T List) |
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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 ![](FONT/eq.png) n < ||l|| ![](FONT/eq.png) l[n] A |
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col_member |
Def x c == c(x) |
| | Thm* T:Type, x:T, c:Collection(T). x c 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|| ![](FONT/int.png) |
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Thm* ||nil|| ![](FONT/int.png) |
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nat |
Def == {i: | 0 i } |
| | Thm* Type |
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nth_tl |
Def nth_tl(n;as) == if n![](FONT/le.png) 0 as else nth_tl(n-1;tl(as)) fi (recursive) |
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Thm* A:Type, as:A List, i: . nth_tl(i;as) A List |
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hd |
Def hd(l) == Case of l; nil "?" ; h.t h |
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Thm* A:Type, l:A List. ||l|| 1 ![](FONT/eq.png) hd(l) A |
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le |
Def A B == B < A |
| | Thm* i,j: . (i j) Prop |
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tl |
Def tl(l) == Case of l; nil nil ; h.t t |
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Thm* A:Type, l:A List. tl(l) A List |
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le_int |
Def i![](FONT/le.png) j == ![](FONT/not.png) j < i |
| | Thm* i,j: . (i![](FONT/le.png) j) ![](FONT/bool.png) |
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not |
Def A == A ![](FONT/eq.png) False |
| | Thm* A:Prop. ( A) Prop |
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lt_int |
Def i < j == if i < j true ; false fi |
| | Thm* i,j: . (i < j) ![](FONT/bool.png) |
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bnot |
Def ![](FONT/not.png) b == if b false else true fi |
| | Thm* b: . ![](FONT/not.png) b ![](FONT/bool.png) |