| Who Cites col list prod? |
|
col_list_prod | Def col_list_prod(l)(x) == ||x|| = ||l|| & ( i: . i < ||x||  x[i] l[i]) |
| | Thm* T:Type, l:Collection(T) List. col_list_prod(l) Collection(T List) |
|
select |
Def l[i] == hd(nth_tl(i;l)) |
| |
Thm* A:Type, l:A List, n: . 0 n  n < ||l||  l[n] A |
|
col_member |
Def x c == c(x) |
| | Thm* T:Type, x:T, c:Collection(T). x c Prop |
|
length |
Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive) |
| |
Thm* A:Type, l:A List. ||l||  |
| |
Thm* ||nil||  |
|
nat |
Def == {i: | 0 i } |
| | Thm* Type |
|
nth_tl |
Def nth_tl(n;as) == if n 0 as else nth_tl(n-1;tl(as)) fi (recursive) |
| |
Thm* A:Type, as:A List, i: . nth_tl(i;as) A List |
|
hd |
Def hd(l) == Case of l; nil "?" ; h.t h |
| |
Thm* A:Type, l:A List. ||l|| 1  hd(l) A |
|
le |
Def A B == B < A |
| | Thm* i,j: . (i j) Prop |
|
tl |
Def tl(l) == Case of l; nil nil ; h.t t |
| |
Thm* A:Type, l:A List. tl(l) A List |
|
le_int |
Def i j ==  j < i |
| | Thm* i,j: . (i j)  |
|
not |
Def A == A  False |
| | Thm* A:Prop. ( A) Prop |
|
lt_int |
Def i < j == if i < j true ; false fi |
| | Thm* i,j: . (i < j)  |
|
bnot |
Def  b == if b false else true fi |
| | Thm* b: .  b  |