| | Some definitions of interest. |
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| hall | Def all ==  p:'a   .   x:'a. (p(x)) |
| | | Thm* 'a:S. all  (('a hbool) hbool) |
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| ball | Def x:T. P(x) ==  (x:T.  P(x)) |
| | | Thm* T:Type, P:(T). (x:T. P(x)) |
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| hselect | Def select == p:'a. @x:'a. (p(x)) |
| | | Thm* 'a:S. select (('a hbool) 'a) |
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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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| hexists | Def exists == p:'a.  x:'a. (p(x)) |
| | | Thm* 'a:S. exists (('a hbool) hbool) |
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| his_pair | Def is_pair == p:'a'b. x:'a. y:'b. (p = (mk_pair(x,y))) |
| | | Thm* 'a,'b:S. is_pair (('a 'b hbool) hbool) |
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| bexists | Def x:T. P(x) == (x:T. P(x)) |
| | | Thm* T:Type, P:(T). (x:T. P(x)) |
|
| assert | Def b == if b True else False fi |
| | | Thm* b:. b Prop |
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| hand | Def and == p:. q:. p  q |
| | | Thm* and (hbool hbool hbool) |
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| hrep_prod | Def rep_prod == p:'a 'b. mk_pair(1of(p),2of(p)) |
| | | Thm* 'a,'b:S. rep_prod (hprod('a; 'b) 'a 'b hbool) |
|
| band | Def pq == if p q else false fi |
| | | Thm* p,q:. (pq) |
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| hequal | Def equal == x:'a. y:'a. x = y |
| | | Thm* 'a:S. equal ('a 'a hbool) |
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| bequal | Def x = y == (x = y T) |
| | | Thm* T:Type, x,y:T. (x = y) |
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| himplies | Def implies == p:. q:. p  q |
| | | Thm* implies (hbool hbool hbool) |
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| bimplies | Def pq ==  p  q |
| | | Thm* p,q:. pq |
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| hbool | Def hbool == |
| | | Thm* hbool S |
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| hfun | Def 'a 'b == 'a'b |
| | | Thm* 'a,'b:S. ('a 'b) S |
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| hprod | Def hprod('a; 'b) == 'a'b |
| | | Thm* 'a,'b:S. hprod('a; 'b) S |
|
| label | Def t ...$L == t |
|
| stype | Def S == {T:Type| x:T. True } |
| | | Thm* S Type{2} |
|
| tlambda | Def (x:T. b(x))(x) == b(x) |
