| | Some definitions of interest. |
|
| happend | Def append ==  l1:'a List. l2:'a List. l1 @ l2 |
| | | Thm*  'a:S. append  (hlist('a)   hlist('a) hlist('a)) |
|
| append | Def as @ bs == Case of as; nil  bs ; a.as' cons(a; (as' @ bs)) (recursive) |
| | | Thm* T:Type, as,bs:T List. (as @ bs) T List |
|
| 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) |
|
| hadd | Def add == m: . n:. m+n |
|
| hlength | Def length == l:'a List. ||l|| |
| | | Thm* 'a:S. length (hlist('a) hnum) |
|
| hlist | Def hlist('a) == 'a List |
| | | Thm* 'a:S. hlist('a) S |
|
| hnum | Def hnum == |
| | | Thm* hnum S |
|
| length | Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive) |
| | | Thm* A:Type, l:A List. ||l||  |
| | | Thm* ||nil|| |
| | | Thm* 'a:Type, l:'a List. ||l|| |
|
| 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) |
