| Who Cites his list rep? |
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his_list_rep | Def is_list_rep
Def == r:(  'a) .  f:  'a
Def == r:(  'a) .    n:
Def == r:(  'a) .    (r
Def == r:(  'a) .    = < m: . if m< n then f(m) else @ x:'a. true fi ,n>) |
| | Thm* 'a:S. is_list_rep (hprod((hnum  'a); hnum)  hbool) |
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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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lt_int | Def i< j == if i<j true ; false fi |
| | Thm* i,j: . (i< j)  |
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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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nat | Def == {i: | 0 i } |
| | Thm* Type |
| | Thm* S |
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tlambda | Def ( x:T. b(x))(x) == b(x) |
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bequal | Def x = y ==  (x = y T) |
| | Thm* T:Type, x,y:T. (x = y)  |
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bexists | Def  x:T. P(x) ==  ( x:T. P(x)) |
| | Thm* T:Type, P:(T  ). ( x:T. P(x))  |
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assert | Def b == if b True else False fi |
| | Thm* b: . b Prop |
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choose | Def @x:T. P(x) == InjCase(lem({x:T| P(x) }); x. x, arb(T)) |
| | Thm* T:S, P:(T Type). (@x:T. P(x)) T |
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le | Def A B == B<A |
| | Thm* i,j: . (i j) Prop |
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prop_to_bool | Def  P == InjCase(lem(P) ; true ; false ) |
| | Thm* P:Prop. ( P)  |
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arb | Def arb(T) == InjCase(lem(T); x. x, "uu") |
| | Thm* T:S. arb(T) T |
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not | Def A == A  False |
| | Thm* A:Prop. ( A) Prop |