| | Some definitions of interest. |
|
| 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 |
|
| band | Def p  q == if p q else false fi |
| | | Thm* p,q:. (pq) |
|
| bequal | Def x = y == (x = y T) |
| | | Thm* T:Type, x,y:T. (x = y) |
|
| prop_to_bool | Def P == InjCase(lem(P) ; true; false) |
| | | Thm* P:Prop. (P) |
|
| 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} |
