| | Some definitions of interest. |
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| rep_list | Def rep_list('a;l) == < n: . if n< ||l|| then l[n] else arb('a) fi ,||l||> |
| | | Thm*  'a:S, l:'a List. rep_list('a;l)  (  'a) |
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| arb | Def arb(T) == InjCase(lem(T); x. x, "uu") |
| | | Thm* T:S. arb(T) T |
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| bequal | Def x = y ==  (x = y T) |
| | | Thm* T:Type, x,y:T. (x = y)  |
|
| pre | Def pre(n) == if n=0 then 0 else n-1 fi |
| | | Thm* n:. pre(n) |
|
| bif | Def bif(b; bx.x(bx); by.y(by)) == if b x(*) else y(x.x) fi |
| | | Thm* A:Type, b:, x:(bA), y:(( b)A). bif(b; bx.x(bx); by.y(by)) A |
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| hlist | Def hlist('a) == 'a List |
| | | Thm* 'a:S. hlist('a) S |
|
| length | Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive) |
| | | Thm* A:Type, l:A List. ||l||  |
| | | Thm* ||nil|| |
| | | Thm* 'a:Type, l:'a List. ||l|| |
|
| select | Def l[i] == hd(nth_tl(i;l)) |
| | | Thm* A:Type, l:A List, n:. 0 n   n<||l|| l[n] A |
|
| lt_int | Def i<j == if i<j true ; false fi |
| | | Thm* i,j:. (i<j) |
|
| nat | Def == {i:| 0i } |
| | | Thm* Type |
| | | Thm* S |
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| pi1 | Def 1of(t) == t.1 |
| | | Thm* A:Type, B:(AType), p:(a:AB(a)). 1of(p) A |
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| pi2 | Def 2of(t) == t.2 |
| | | Thm* A:Type, B:(AType), p:(a:AB(a)). 2of(p) B(1of(p)) |
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| stype | Def S == {T:Type|  x:T. True } |
| | | Thm* S Type{2} |
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| tlambda | Def (x:T. b(x))(x) == b(x) |
