| | Who Cites l interval? |
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| l_interval | Def l_interval(l;j;i) == mklist(i-j; x.l[(j+x)]) |
| | | Thm*  T:Type, l:T List, i: ||l||, j:(i+1). l_interval(l;j;i)  T List |
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| select | Def l[i] == hd(nth_tl(i;l)) |
| | | Thm* A:Type, l:A List, n: . 0 n   n<||l|| l[n] A |
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| mklist | Def mklist(n;f) == primrec(n;nil;i,l. l @ [(f(i))]) |
| | | Thm* T:Type, n:, f:(n  T). mklist(n;f) T List |
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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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| append | Def as @ bs == Case of as; nil bs ; a.as' [a / (as' @ bs)] (recursive) |
| | | Thm* T:Type, as,bs:T List. (as @ bs) T List |
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| primrec | Def primrec(n;b;c) == if n=0 b else c(n-1,primrec(n-1;b;c)) fi (recursive) |
| | | Thm* T:Type, n:, b:T, c:(nTT). primrec(n;b;c) T |
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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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| eq_int | Def i=j == if i=j true ; false fi |
| | | Thm* i,j:. (i=j) |
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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 |
