| | Some definitions of interest. |
|
| his_pair | Def is_pair ==  p:'a  'b .   x:'a. y:'b. (p = (mk_pair(x,y))) |
| | | Thm*  'a,'b:S. is_pair  (('a 'b hbool) hbool) |
|
| assert | Def  b == if b True else False fi |
| | | Thm* b:. b Prop |
|
| hbool | Def hbool == |
| | | Thm* hbool S |
|
| 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) |
|
| hprod | Def hprod('a; 'b) == 'a'b |
| | | Thm* 'a,'b:S. hprod('a; 'b) S |
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| 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} |
