| | Some definitions of interest. |
|
| inject | Def Inj(A; B; f) ==  a1,a2:A. f(a1) = f(a2)  B   a1 = a2 |
| | | Thm* A,B:Type, f:(A  B). Inj(A; B; f) Prop |
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| int_seg | Def {i..j } == {k: | i  k < j } |
| | | Thm* m,n:. {m..n} Type |
|
| l_member | Def (x l) ==  i: . i < ||l|| & x = l[i] T |
| | | Thm* T:Type, x:T, l:T List. (x l) Prop |
|
| no_repeats | Def no_repeats(T;l) == i,j:. i < ||l|| j < ||l||  i = j l[i] = l[j] T |
| | | Thm* T:Type, l:T List. no_repeats(T;l) Prop |
|
| length | Def ||as|| == Case of as; nil  0 ; a.as' ||as'||+1 (recursive) |
| | | Thm* A:Type, l:A List. ||l|| |
| | | Thm* ||nil|| |
|
| pi1 | Def 1of(t) == t.1 |
| | | Thm* A:Type, B:(AType), p:(a:A B(a)). 1of(p) A |
|
| select | Def l[i] == hd(nth_tl(i;l)) |
| | | Thm* A:Type, l:A List, n:. 0n n < ||l|| l[n] A |
