| Who Cites hprim rec fun? |
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hprim_rec_fun | Def prim_rec_fun
Def == x:'a. f:'a    'a. simp_rec
Def == x:'a. f:'a    'a. (( n: . x)
Def == x:'a. f:'a    'a. , fun:  'a. n: . f(fun(pre(n)),n)) |
| | Thm* 'a:S. prim_rec_fun ('a  ('a  hnum  'a)  hnum  hnum  'a) |
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pre | Def pre(n) == if n= 0 then 0 else n-1 fi |
| | Thm* n: . pre(n)  |
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hnum | Def hnum ==  |
| | Thm* hnum S |
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hsimp_rec | Def simp_rec == x:'a. f:'a 'a. n: . ncompose(f;n;x) |
| | Thm* 'a:S. simp_rec ('a  ('a  'a)  hnum  '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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hfun | Def 'a  'b == 'a 'b |
| | Thm* 'a,'b:S. ('a  'b) S |
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ncompose | Def ncompose(f;n;x) == if n= 0 then x else f(ncompose(f;n-1;x)) fi (recursive) |
| | Thm* 'a:Type, n: , x:'a, f:('a 'a). ncompose(f;n;x) 'a |
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eq_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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le | Def A B == B<A |
| | Thm* i,j: . (i j) Prop |
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not | Def A == A  False |
| | Thm* A:Prop. ( A) Prop |