| | Some definitions of interest. |
|
| hall | Def all ==  p:'a   .   x:'a. (p(x)) |
| | | Thm* 'a:S. all  (('a hbool) hbool) |
|
| assert | Def  b == if b True else False fi |
| | | Thm* b:. b Prop |
|
| habs_sum | Def abs_sum == f:'a'b. @u:'a+'b. (rep_sum(u) = f 'a'b) |
| | | Thm* 'a,'b:S. abs_sum ((hbool 'a 'b hbool) hsum('a; 'b)) |
|
| 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) |
|
| 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) |
|
| hnot | Def not == p:.  p |
| | | Thm* not (hbool hbool) |
|
| bnot | Def b == if b false else true fi |
| | | Thm* b:. b |
|
| hbool | Def hbool == |
| | | Thm* hbool S |
|
| hinr | Def inr == x:'b. inr(x) |
| | | Thm* 'b,'a:S. inr ('b hsum('a; 'b)) |
|
| hsum | Def hsum('a; 'b) == 'a+'b |
| | | Thm* 'a,'b:S. hsum('a; 'b) S |
|
| stype | Def S == {T:Type|  x:T. True } |
| | | Thm* S Type{2} |
|
| tlambda | Def (x:T. b(x))(x) == b(x) |
