| | Some definitions of interest. |
|
| ball | Def   x:T. P(x) ==  (x:T.  P(x)) |
| | | Thm* T:Type, P:(T   ). (x:T. P(x))  |
|
| 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) |
|
| 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) |
|
| band | Def pq == if p q else false fi |
| | | Thm* p,q:. (pq) |
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| bchoose | Def @x:'a. p(x) == @x:'a. p(x) |
| | | Thm* 'a:S, p:('a). (@x:'a. p(x)) 'a |
|
| bequal | Def x = y == (x = y T) |
| | | Thm* T:Type, x,y:T. (x = y) |
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| bexists | Def x:T. P(x) == (x:T. P(x)) |
| | | Thm* T:Type, P:(T). (x:T. P(x)) |
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| bimplies | Def p  q ==  p  q |
| | | Thm* p,q:. pq |
|
| hbool | Def hbool == |
| | | Thm* hbool S |
|
| hfun | Def 'a 'b == 'a'b |
| | | Thm* 'a,'b:S. ('a 'b) S |
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| hprod | Def hprod('a; 'b) == 'a'b |
| | | Thm* 'a,'b:S. hprod('a; 'b) S |
|
| 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) |
