| | Some definitions of interest. |
|
| hall | Def all ==  p:'a   .   x:'a. (p(x)) |
| | | Thm* 'a:S. all  (('a hbool) hbool) |
|
| hexists | Def exists == p:'a.  x:'a. (p(x)) |
| | | Thm* 'a:S. exists (('a hbool) hbool) |
|
| 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) |
|
| assert | Def  b == if b True else False fi |
| | | Thm* b:. b Prop |
|
| 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 |
|
| hmk_pair | Def mk_pair == x:'a. y:'b. a:'a. b:'b. (a = x)  (b = y) |
| | | Thm* 'a,'b:S. mk_pair ('a 'b 'a 'b hbool) |
|
| stype | Def S == {T:Type| x:T. True } |
| | | Thm* S Type{2} |
|
| tlambda | Def (x:T. b(x))(x) == b(x) |
