| | 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) |
|
| hcond | Def cond == b:. p:'a. q:'a. if b then p else q fi |
| | | Thm* 'a:S. cond (hbool 'a 'a 'a) |
|
| hsub | Def sub == m: . n:. nnsub(m;n) |
| | | Thm* sub (hnum hnum hnum) |
|
| nnsub | Def nnsub(m;n) == if m< n then 0 else m-n fi |
| | | Thm* m,n:. nnsub(m;n) |
|
| bif | Def bif(b; bx.x(bx); by.y(by)) == if b x(*) else y(x.x) fi |
| | | Thm* A:Type, b:, x:(bA), y:(( b)A). bif(b; bx.x(bx); by.y(by)) A |
|
| hle | Def le == m:. n:. m n |
| | | Thm* le (hnum hnum hbool) |
|
| hnum | Def hnum == |
| | | Thm* hnum S |
|
| hsuc | Def suc == n:. n+1 |
| | | Thm* suc (hnum hnum) |
|
| le_int | Def ij == j<i |
| | | Thm* i,j: . (ij) |
|
| nat | Def == {i:| 0i } |
| | | Thm* Type |
| | | Thm* S |
|
| tlambda | Def (x:T. b(x))(x) == b(x) |
