| | 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) |
|
| hfst | Def fst == p:'a 'b. 1of(p) |
| | | Thm* 'a,'b:S. fst (hprod('a; 'b) 'a) |
|
| hpair | Def pair == x:'a. y:'b. <x,y> |
| | | Thm* 'a,'b:S. pair ('a 'b hprod('a; 'b)) |
|
| hprod | Def hprod('a; 'b) == 'a'b |
| | | Thm* 'a,'b:S. hprod('a; 'b) S |
|
| hsnd | Def snd == p:'a'b. 2of(p) |
| | | Thm* 'a,'b:S. snd (hprod('a; 'b) 'b) |
|
| pi1 | Def 1of(t) == t.1 |
| | | Thm* A:Type, B:(AType), p:(a:AB(a)). 1of(p) A |
|
| pi2 | Def 2of(t) == t.2 |
| | | Thm* A:Type, B:(AType), p:(a:AB(a)). 2of(p) B(1of(p)) |
|
| stype | Def S == {T:Type|  x:T. True } |
| | | Thm* S Type{2} |
|
| tlambda | Def (x:T. b(x))(x) == b(x) |
