| | Some definitions of interest. |
|
| bchoose | Def @ x:'a. p(x) == @x:'a.  p(x) |
| | | Thm*  'a:S, p:('a   ). (@x:'a. p(x))  'a |
|
| assert | Def b == if b True else False fi |
| | | Thm* b:. b Prop |
|
| hrep_prod | Def rep_prod ==  p:'a 'b. mk_pair(1of(p),2of(p)) |
| | | Thm* 'a,'b:S. rep_prod (hprod('a; 'b) 'a 'b hbool) |
|
| hmk_pair | Def mk_pair == x:'a. y:'b. a:'a. b:'b. (a = x)  (b = y) |
| | | Thm* 'a,'b:S. mk_pair ('a 'b 'a 'b hbool) |
|
| bequal | Def x = y ==  (x = y T) |
| | | Thm* T:Type, x,y:T. (x = y) |
|
| choose | Def @x:T. P(x) == InjCase(lem({x:T| P(x) }); x. x, arb(T)) |
| | | Thm* T:S, P:(TType). (@x:T. P(x)) T |
|
| hbool | Def hbool == |
| | | Thm* hbool S |
|
| hfun | Def 'a 'b == 'a'b |
| | | Thm* 'a,'b:S. ('a 'b) S |
|
| hprod | Def hprod('a; 'b) == 'a'b |
| | | Thm* 'a,'b:S. hprod('a; 'b) S |
|
| stype | Def S == {T:Type|  x:T. True } |
| | | Thm* S Type{2} |
