| | 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 |
|
| 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) |
|
| hadd | Def add == m: . n:. m+n |
| | | Thm* add (hnum hnum hnum) |
|
| hdiv | Def div == m:. n:. ndiv(m;n) |
| | | Thm* div (hnum hnum hnum) |
|
| himplies | Def implies == p:. q:. p   q |
| | | Thm* implies (hbool hbool hbool) |
|
| hlt | Def lt == m:. n:. m<n |
| | | Thm* lt (hnum hnum hbool) |
|
| hmult | Def mult == m:. n:. m n |
| | | Thm* mult (hnum hnum hnum) |
|
| hnum | Def hnum == |
| | | Thm* hnum S |
|
| nat | Def == {i: | 0 i } |
| | | Thm* Type |
| | | Thm* S |
|
| ndiv | Def ndiv(m;n) == if n=0 then 0 else m  n fi |
| | | Thm* m,n:. ndiv(m;n) |
|
| tlambda | Def (x:T. b(x))(x) == b(x) |
