| | 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_num | Def abs_num == n: . @m:. (n = rep_num(m) ) |
| | | Thm* abs_num (hind hnum) |
|
| hequal | Def equal == x:'a. y:'a. x = y |
| | | Thm* 'a:S. equal ('a 'a hbool) |
|
| hnum | Def hnum == |
| | | Thm* hnum S |
|
| hrep_num | Def rep_num == n:. ncompose(suc_rep;n;zero_rep) |
| | | Thm* rep_num (hnum hind) |
|
| hsuc | Def suc == n:. n+1 |
| | | Thm* suc (hnum hnum) |
|
| hsuc_rep | Def suc_rep == x:. (@f:. (one_one(;;f) &  onto(;;f)))(x) |
| | | Thm* suc_rep (hind hind) |
|
| nat | Def == {i: | 0 i } |
| | | Thm* Type |
| | | Thm* S |
|
| tlambda | Def (x:T. b(x))(x) == b(x) |
