| | Some definitions of interest. |
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| arrows | Def r- > L^k ==  n: . r n   (G:({s:(n List)| ||s|| = k   & (x,y:||s||. x < y s[x] < s[y]) }  ||L||).  c:||L||, f:(L[c]n). increasing(f;L[c]) & (s:L[c] List. ||s|| = k (x,y:||s||. x < y s[x] < s[y]) G(map(f;s)) = c)) |
| | | Thm* r:, k:, L: List. r- > L^k Prop |
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| increasing | Def increasing(f;k) == i:(k-1). f(i) < f(i+1) |
| | | Thm* k:, f:(k). increasing(f;k) Prop |
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| int_seg | Def {i..j } == {k:| i k < j } |
| | | Thm* m,n:. {m..n} Type |
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| nat | Def == {i:| 0i } |
| | | Thm* Type |
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| le | Def AB ==  B < A |
| | | Thm* i,j:. (ij) Prop |
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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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| map | Def map(f;as) == Case of as; nil nil ; a.as' [(f(a)) / map(f;as')] (recursive) |
| | | Thm* A,B:Type, f:(AB), l:A List. map(f;l) B List |
| | | Thm* A,B:Type, f:(AB), l:A List . map(f;l) B List |
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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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| sum | Def sum(f(x) | x < k) == primrec(k;0; x,n. n+f(x)) |
| | | Thm* n:, f:(n). sum(f(x) | x < n) |
