| | 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) |
|
| hand | Def and == p:. q:. p  q |
| | | Thm* and (hbool hbool hbool) |
|
| hfun | Def 'a 'b == 'a'b |
| | | Thm* 'a,'b:S. ('a 'b) S |
|
| hnum | Def hnum ==  |
| | | Thm* hnum S |
|
| hsimp_rec | Def simp_rec == x:'a. f:'a'a. n:. ncompose(f;n;x) |
| | | Thm* 'a:S. simp_rec ('a ('a 'a) hnum 'a) |
|
| hsuc | Def suc == n:. n+1 |
| | | Thm* suc (hnum hnum) |
|
| nat | Def == {i: | 0 i } |
| | | Thm* Type |
| | | Thm* S |
|
| stype | Def S == {T:Type|  x:T. True } |
| | | Thm* S Type{2} |
|
| tlambda | Def (x:T. b(x))(x) == b(x) |
