| | 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) |
|
| hinr | Def inr == x:'b. inr(x) |
| | | Thm* 'b,'a:S. inr ('b hsum('a; 'b)) |
|
| hisr | Def isr == u:'a+'b. isr(u) |
| | | Thm* 'a,'b:S. isr (hsum('a; 'b) hbool) |
|
| houtr | Def outr == u:'a+'b. InjCase(u; x. arb('b), x) |
| | | Thm* 'a,'b:S. outr (hsum('a; 'b) 'b) |
|
| hsum | Def hsum('a; 'b) == 'a+'b |
| | | Thm* 'a,'b:S. hsum('a; 'b) S |
|
| isr | Def isr(x) == InjCase(x; y. false; z. true) |
| | | Thm* A,B:Type, x:A+B. isr(x) |
|
| outr | Def outr(x) == InjCase(x; y. "???"; z. z) |
| | | Thm* A,B:Type, x:A+B.  isl(x) outr(x) B |
|
| stype | Def S == {T:Type|  x:T. True } |
| | | Thm* S Type{2} |
|
| tlambda | Def (x:T. b(x))(x) == b(x) |
