| | Who Cites l disjoint? |
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| l_disjoint | Def l_disjoint(T;l1;l2) ==  x:T.  ((x  l1) & (x l2)) |
| | | Thm* T:Type, l,l':T List. l_disjoint(T;l;l') 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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| nat | Def == {i: | 0 i } |
| | | Thm* Type |
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| le | Def AB == B<A |
| | | Thm* i,j:. (ij) Prop |
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| not | Def A == A   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:. 0n n<||l|| l[n] A |
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| length | Def ||as|| == Case of as; nil  0 ; a.as' ||as'||+1 (recursive) |
| | | Thm* A:Type, l:A List. ||l|| |
| | | Thm* ||nil|| |
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| nth_tl | Def nth_tl(n;as) == if n 0 as else nth_tl(n-1;tl(as)) fi (recursive) |
| | | 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 |
| | | Thm* A:Type, l:A List. ||l|| 1 hd(l) A |
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| tl | Def tl(l) == Case of l; nil nil ; h.t t |
| | | 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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| 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 |
