| | 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) |
|
| himplies | Def implies == p:. q:. p   q |
| | | Thm* implies (hbool hbool hbool) |
|
| hinl | Def inl == x:'a. inl(x) |
| | | Thm* 'a,'b:S. inl ('a hsum('a; 'b)) |
|
| hisl | Def isl == u:'a+'b. isl(u) |
| | | Thm* 'a,'b:S. isl (hsum('a; 'b) hbool) |
|
| houtl | Def outl == u:'a+'b. InjCase(u; x. x, arb('a)) |
| | | Thm* 'a,'b:S. outl (hsum('a; 'b) 'a) |
|
| hsum | Def hsum('a; 'b) == 'a+'b |
| | | Thm* 'a,'b:S. hsum('a; 'b) S |
|
| isl | Def isl(x) == InjCase(x; y. true; z. false) |
| | | Thm* A,B:Type, x:A+B. isl(x) |
|
| outl | Def outl(x) == InjCase(x; y. y; z. "???") |
| | | Thm* A,B:Type, x:A+B. isl(x) outl(x) A |
|
| stype | Def S == {T:Type|  x:T. True } |
| | | Thm* S Type{2} |
|
| tlambda | Def (x:T. b(x))(x) == b(x) |
