| Who Cites sublist? |
|
sublist | Def sublist(T;L1;L2)
== f:(||L1||||L2||). increasing(f;||L1||) & (j:||L1||. L1[j] = L2[(f(j))] T) |
| | Thm* T:Type, L1,L2:T List. sublist(T;L1;L2) Prop |
|
select |
Def l[i] == hd(nth_tl(i;l)) |
| |
Thm* A:Type, l:A List, n:. 0n n < ||l|| l[n] A |
|
length |
Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive) |
| |
Thm* A:Type, l:A List. ||l|| |
| |
Thm* ||nil|| |
|
increasing |
Def increasing(f;k) == i:(k-1). f(i) < f(i+1) |
| | Thm* k:, f:(k). increasing(f;k) Prop |
|
int_seg |
Def {i..j} == {k:| i k < j } |
| | Thm* m,n:. {m..n} Type |
|
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 |
|
hd |
Def hd(l) == Case of l; nil "?" ; h.t h |
| |
Thm* A:Type, l:A List. ||l||1 hd(l) A |
| |
Thm* A:Type, l:A List. hd(l) A |
|
lelt |
Def i j < k == ij & j < k |
|
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 ij == j < i |
| | Thm* i,j:. (ij) |
|
le |
Def AB == B < A |
| | Thm* i,j:. (ij) 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 |
|
not |
Def A == A False |
| | Thm* A:Prop. (A) Prop |