| | 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 |
|
| hcons | Def cons == x:'a. l:'a List. cons(x; l) |
| | | Thm* 'a:S. cons ('a hlist('a) hlist('a)) |
|
| hhd | Def hd == l:'a List. if null(l) then arb('a) else head(l) fi |
| | | Thm* 'a:S. hd (hlist('a) 'a) |
|
| head | Def head(l) == hd(l) |
| | | Thm* 'a:Type, l:'a List.  mt(l)   head(l) 'a |
|
| hequal | Def equal == x:'a. y:'a. x = y |
| | | Thm* 'a:S. equal ('a 'a hbool) |
|
| himplies | Def implies == p:. q:. p q |
| | | Thm* implies (hbool hbool hbool) |
|
| hlist | Def hlist('a) == 'a List |
| | | Thm* 'a:S. hlist('a) S |
|
| hnot | Def not == p:. p |
| | | Thm* not (hbool hbool) |
|
| hnull | Def null == l:'a List. null(l) |
| | | Thm* 'a:S. null (hlist('a) hbool) |
|
| htl | Def tl == l:'a List. tl(l) |
| | | Thm* 'a:S. tl (hlist('a) hlist('a)) |
|
| mt | Def mt(l) == Case of l; nil True ; a.as' False |
| | | Thm* 'a:Type{i}, l:'a List. mt(l) Prop{1} |
|
| not | Def A == A False |
| | | Thm* A:Prop. (A) Prop |
|
| stype | Def S == {T:Type|  x:T. True } |
| | | Thm* S Type{2} |
|
| tl | Def tl(l) == Case of l; nil nil ; h.t t |
| | | Thm* A:Type, l:A List. tl(l) A List |
|
| tlambda | Def (x:T. b(x))(x) == b(x) |
