| | Some definitions of interest. |
|
| hall | Def all == p:'a  .  x:'a. (p(x)) |
| | | Thm* 'a:S. all (('a  hbool)  hbool) |
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| hexists | Def exists == p:'a  .  x:'a. (p(x)) |
| | | Thm* 'a:S. exists (('a  hbool)  hbool) |
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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) |
|
| hselect | Def select == p:'a  . @ x:'a. (p(x)) |
| | | Thm* 'a:S. select (('a  hbool)  'a) |
|
| assert | Def b == if b True else False fi |
| | | Thm* b: . b Prop |
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| hbool | Def hbool ==  |
| | | Thm* hbool S |
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| hcond | Def cond == b: . p:'a. q:'a. if b then p else q fi |
| | | Thm* 'a:S. cond (hbool  'a  'a  'a) |
|
| hequal | Def equal == x:'a. y:'a. x = y |
| | | Thm* 'a:S. equal ('a  'a  hbool) |
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| hfun | Def 'a  'b == 'a 'b |
| | | Thm* 'a,'b:S. ('a  'b) S |
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| hlt | Def lt == m: . n: . m< n |
| | | Thm* lt (hnum  hnum  hbool) |
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| hnum | Def hnum ==  |
| | | Thm* hnum S |
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| hpair | Def pair == x:'a. y:'b. <x,y> |
| | | Thm* 'a,'b:S. pair ('a  'b  hprod('a; 'b)) |
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| hprod | Def hprod('a; 'b) == 'a 'b |
| | | Thm* 'a,'b:S. hprod('a; 'b) S |
|
| ht | Def t == true |
| | | Thm* t hbool |
|
| label | Def t ...$L == t |
|
| 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) |