| | Some definitions of interest. |
|
| hall | Def all ==  p:'a   .   x:'a. (p(x)) |
| | | Thm* 'a:S. all  (('a hbool) hbool) |
|
| ball | Def x:T. P(x) ==  (x:T.  P(x)) |
| | | Thm* T:Type, P:(T). (x:T. P(x)) |
|
| 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)) |
|
| assert | Def b == if b True else False fi |
| | | Thm* b:. b Prop |
|
| hequal | Def equal == x:'a. y:'a. x = y |
| | | Thm* 'a:S. equal ('a 'a hbool) |
|
| bequal | Def x = y == (x = y T) |
| | | Thm* T:Type, x,y:T. (x = y) |
|
| hbool | Def hbool == |
| | | Thm* hbool S |
|
| hfun | Def 'a 'b == 'a'b |
| | | Thm* 'a,'b:S. ('a 'b) S |
|
| honto | Def onto == f:'a'b. onto('a;'b;f) |
| | | Thm* 'a,'b:S. onto (('a 'b) hbool) |
|
| onto | Def onto('a;'b;f) == y:'b. x:'a. y = f(x) |
| | | Thm* 'a,'b:Type, f:('a'b). onto('a;'b;f) Prop |
|
| prop_to_bool | Def P == InjCase(lem(P) ; true ; false) |
| | | Thm* P:Prop. (P) |
|
| stype | Def S == {T:Type| x:T. True } |
| | | Thm* S Type{2} |
|
| tlambda | Def (x:T. b(x))(x) == b(x) |
