| | Some definitions of interest. |
|
| hselect | Def select ==  p:'a   . @ x:'a. (p(x)) |
| | | Thm*  'a:S. select  (('a hbool) 'a) |
|
| bchoose | Def @x:'a. p(x) == @x:'a.  p(x) |
| | | Thm* 'a:S, p:('a). (@x:'a. p(x)) 'a |
|
| harb | Def arb == arb('a) |
| | | Thm* 'a:S. arb 'a |
|
| arb | Def arb(T) == InjCase(lem(T); x. x, "uu") |
| | | Thm* T:S. arb(T) T |
|
| assert | Def b == if b True else False fi |
| | | Thm* b:. b Prop |
|
| bif | Def bif(b; bx.x(bx); by.y(by)) == if b x(*) else y(x.x) fi |
| | | Thm* A:Type, b:, x:(bA), y:(( b)A). bif(b; bx.x(bx); by.y(by)) A |
|
| hequal | Def equal == x:'a. y:'a. x = y |
| | | Thm* 'a:S. equal ('a 'a hbool) |
|
| ht | Def t == true |
| | | Thm* t hbool |
|
| label | Def t ...$L == t |
|
| length | Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive) |
| | | Thm* A:Type, l:A List. ||l||  |
| | | Thm* ||nil|| |
| | | Thm* 'a:Type, l:'a List. ||l||  |
|
| listify | Def f{m..n } == if n m nil else cons((f(m)); (f{(m+1)..n})) fi (recursive) |
| | | Thm* T:Type, m,n:, f:({m..n}T). f{m..n} T List |
|
| lt_int | Def i<j == if i<j true ; false fi |
| | | Thm* i,j:. (i<j) |
|
| nat | Def == {i:| 0i } |
| | | Thm* Type |
| | | Thm* S |
|
| not | Def A == A   False |
| | | Thm* A:Prop. (A) Prop |
|
| stype | Def S == {T:Type|  x:T. True } |
| | | Thm* S Type{2} |
|
| tlambda | Def (x:T. b(x))(x) == b(x) |
