| | 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 |
|
| hnot | Def not == p:.   p |
| | | Thm* not (hbool hbool) |
|
| hodd | Def odd == n: . odd(n) |
| | | Thm* odd (hnum hbool) |
|
| odd | Def odd(n) == if n=0 then false else odd(n-1) fi (recursive) |
| | | Thm* n:. odd(n) |
|
| bnot | Def b == if b false else true fi |
| | | Thm* b:. b |
|
| hand | Def and == p:. q:. p q |
| | | Thm* and (hbool hbool hbool) |
|
| hbool | Def hbool == |
| | | Thm* hbool S |
|
| hequal | Def equal == x:'a. y:'a. x = y |
| | | Thm* 'a:S. equal ('a 'a hbool) |
|
| hf | Def f == false |
| | | Thm* f hbool |
|
| hnum | Def hnum == |
| | | Thm* hnum S |
|
| hsuc | Def suc == n:. n+1 |
| | | Thm* suc (hnum hnum) |
|
| nat | Def == {i: | 0 i } |
| | | Thm* Type |
| | | Thm* S |
|
| tlambda | Def (x:T. b(x))(x) == b(x) |
