| | 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) |
|
| hor | Def or == p:. q:. p   q |
| | | Thm* or (hbool hbool hbool) |
|
| bor | Def p q == if p true else q fi |
| | | Thm* p,q:. (p q) |
|
| hbool | Def hbool == |
| | | Thm* hbool S |
|
| hle | Def le == m: . n:. m n |
| | | Thm* le (hnum hnum hbool) |
|
| hlt | Def lt == m:. n:. m<n |
| | | Thm* lt (hnum hnum hbool) |
|
| hnum | Def hnum == |
| | | Thm* hnum S |
|
| label | Def t ...$L == t |
|
| le_int | Def ij ==  j<i |
| | | Thm* i,j: . (ij) |
|
| lt_int | Def i<j == if i<j true ; false fi |
| | | Thm* i,j:. (i<j) |
|
| nat | Def == {i:| 0i } |
| | | Thm* Type |
| | | Thm* S |
|
| tlambda | Def (x:T. b(x))(x) == b(x) |
