| Who Cites l all? |
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l_all | Def (xL.P(x)) == x:T. (x L) P(x) |
| | Thm* T:Type, L:T List, P:(TProp). (xL.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:. 0n 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:| 0i } |
| | Thm* Type |
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nth_tl |
Def nth_tl(n;as) == if n0 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 AB == B < A |
| | Thm* i,j:. (ij) 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 ij == j < i |
| | Thm* i,j:. (ij) |
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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 |