| | 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 |
|
| int_seg | Def {i..j } == {k:| i k < j } |
| | | Thm* m,n:. {m..n} Type |
|
| nat | Def == {i:| 0i } |
| | | Thm* Type |
|
| 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|| |
|
| nat_plus | Def  == {i:| 0 < i } |
| | | Thm* Type |
|
| not | Def A == A False |
| | | Thm* A:Prop. (A) Prop |
|
| select | Def l[i] == hd(nth_tl(i;l)) |
| | | Thm* A:Type, l:A List, n:. 0n n < ||l|| l[n] A |
|
| sum | Def sum(f(x) | x < k) == primrec(k;0; x,n. n+f(x)) |
| | | Thm* n:, f:(n). sum(f(x) | x < n) |
