| | Some definitions of interest. |
|
| hselect | Def select ==  p:'a   . @ x:'a. (p(x)) |
| | | Thm*  'a:S. select  (('a hbool) 'a) |
|
| bchoose | Def @x:'a. p(x) == @x:'a.  p(x) |
| | | Thm* 'a:S, p:('a). (@x:'a. p(x)) 'a |
|
| hall | Def all == p:'a. x:'a. (p(x)) |
| | | Thm* 'a:S. all (('a hbool) hbool) |
|
| hres_select | Def res_select == P:'a. Q:'a. res_choose('a;x.(P(x));x.(Q(x))) |
| | | Thm* 'a:S. res_select (('a hbool) ('a hbool) 'a) |
|
| 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) |
|
| band | Def pq == if p q else false fi |
| | | Thm* p,q:. (pq) |
|
| 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 |
|
| res_choose | Def res_choose('a;x.P(x);x.Q(x)) == @x:'a. (P(x) & Q(x)) |
| | | Thm* 'a:S, P,Q:('aProp). res_choose('a;x.P(x);x.Q(x)) 'a |
|
| stype | Def S == {T:Type|  x:T. True } |
| | | Thm* S Type{2} |
|
| tlambda | Def (x:T. b(x))(x) == b(x) |
