| | Who Cites habs list? |
|
| habs_list | Def abs_list ==  r:(   'a) . @a:'a List. (r = rep_list('a;a)) |
| | | Thm*  'a:S. abs_list  (hprod((hnum 'a); hnum) hlist('a)) |
|
| rep_list | Def rep_list('a;l) == <n:. if n< ||l|| then l[n] else arb('a) fi ,||l||> |
| | | Thm* 'a:S, l:'a List. rep_list('a;l) ('a) |
|
| nat | Def == {i: | 0 i } |
| | | Thm* Type |
| | | Thm* S |
|
| 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 |
|
| tlambda | Def (x:T. b(x))(x) == b(x) |
|
| 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|| |
|
| arb | Def arb(T) == InjCase(lem(T); x. x, "uu") |
| | | Thm* T:S. arb(T) T |
|
| select | Def l[i] == hd(nth_tl(i;l)) |
| | | Thm* A:Type, l:A List, n:. 0n   n<||l|| l[n] A |
|
| nth_tl | Def nth_tl(n;as) == if n0 as else nth_tl(n-1;tl(as)) fi (recursive) |
| | | Thm* A:Type, as:A List, i:. nth_tl(i;as) A List |
|
| le_int | Def ij ==  j<i |
| | | Thm* i,j:. (ij)  |
|
| lt_int | Def i<j == if i<j true ; false fi |
| | | Thm* i,j:. (i<j) |
|
| 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 |
|
| le | Def AB == B<A |
| | | Thm* i,j:. (ij) Prop |
|
| hd | Def hd(l) == Case of l; nil "?" ; h.t h |
| | | Thm* A:Type, l:A List. ||l|| 1 hd(l) A |
|
| not | Def A == A False |
| | | Thm* A:Prop. (A) Prop |
|
| tl | Def tl(l) == Case of l; nil nil ; h.t t |
| | | Thm* A:Type, l:A List. tl(l) A List |
|
| bnot | Def b == if b false else true fi |
| | | Thm* b:. b |
