| Who Cites l all? |
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l_all | Def ( x L.P(x)) == x:T. (x L)  P(x) |
| | Thm* T:Type, L:T List, P:(T Prop). ( x L.P(x)) 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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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 |
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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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nat |
Def == {i: | 0 i } |
| | Thm* Type |
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nth_tl |
Def nth_tl(n;as) == if n 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  hd(l) A |
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Thm* A:Type, l:A List . 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 j ==  j < i |
| | Thm* i,j: . (i j)  |
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not |
Def A == A  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)  |
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bnot |
Def  b == if b false else true fi |
| | Thm* b: .  b  |