| | Some definitions of interest. |
|
| hexists | Def exists ==  p:'a   .   x:'a. (p(x)) |
| | | Thm*  'a:S. exists  (('a hbool) hbool) |
|
| bexists | Def x:T. P(x) ==  (x:T.  P(x)) |
| | | Thm* T:Type, P:(T). (x:T. P(x)) |
|
| hall | Def all == p:'a. x:'a. (p(x)) |
| | | Thm* 'a:S. all (('a hbool) hbool) |
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| hres_exists | Def res_exists == P:'a. Q:'a. res_exists('a;x.(P(x));x.(Q(x))) |
| | | Thm* 'a:S. res_exists (('a hbool) ('a hbool) hbool) |
|
| assert | Def b == if b True else False fi |
| | | Thm* b:. b Prop |
|
| hand | Def and == p:. q:. p  q |
| | | Thm* and (hbool hbool hbool) |
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| band | Def pq == if p q else false fi |
| | | Thm* p,q:. (pq) |
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| hbool | Def hbool == |
| | | Thm* hbool S |
|
| hequal | Def equal == x:'a. y:'a. x = y |
| | | Thm* 'a:S. equal ('a 'a hbool) |
|
| hfun | Def 'a 'b == 'a'b |
| | | Thm* 'a,'b:S. ('a 'b) S |
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| prop_to_bool | Def P == InjCase(lem(P) ; true; false) |
| | | Thm* P:Prop. (P) |
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| res_exists | Def res_exists('a;x.P(x);x.Q(x)) == x:'a. P(x) & Q(x) |
| | | Thm* 'a:Type, P,Q:('aProp). res_exists('a;x.P(x);x.Q(x)) Prop |
|
| stype | Def S == {T:Type| x:T. True } |
| | | Thm* S Type{2} |
|
| tlambda | Def (x:T. b(x))(x) == b(x) |
