| Some definitions of interest. |
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bchoose | Def @ x:'a. p(x) == @x:'a. p(x) |
| | Thm* 'a:S, p:('a  ). (@ x:'a. p(x)) 'a |
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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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bif | Def bif(b; bx.x(bx); by.y(by)) == if b x(*) else y( x.x) fi |
| | Thm* A:Type, b: , x:(b A), y:(( b) A). bif(b; bx.x(bx); by.y(by)) A |
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label | Def t ...$L == t |
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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||  |
| | Thm* 'a:Type, l:'a List. ||l||  |
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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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lt_int | Def i< j == if i<j true ; false fi |
| | Thm* i,j: . (i< j)  |
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nat | Def == {i: | 0 i } |
| | Thm* Type |
| | Thm* S |
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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) |