| Who Cites swap adjacent? |
|
swap_adjacent | Def swap adjacent[P(x;y)](L1,L2)
Def == i: (||L1||-1). P(L1[i];L1[(i+1)]) & L2 = swap(L1;i;i+1) A List |
| | Thm* A:Type, P:(A A Prop). swap adjacent[P(x,y)] (A List) (A List) Prop |
|
swap | Def swap(L;i;j) == (L o (i, j)) |
| | Thm* T:Type, L:T List, i,j: ||L||. swap(L;i;j) T List |
|
permute_list | Def (L o f) == mklist(||L||; i.L[(f(i))]) |
| | Thm* T:Type, L:T List, f:( ||L||  ||L||). (L o f) 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 |
|
length | Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive) |
| | Thm* A:Type, l:A List. ||l||  |
| | Thm* ||nil||  |
|
int_seg | Def {i..j } == {k: | i k < j } |
| | Thm* m,n: . {m..n } Type |
|
flip | Def (i, j)(x) == if x= i j ; x= j i else x fi |
| | Thm* k: , i,j: k. (i, j) k  k |
|
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 |
|
lelt | Def i j < k == i j & j<k |
|
mklist | Def mklist(n;f) == primrec(n;nil; i,l. l @ [(f(i))]) |
| | Thm* T:Type, n: , f:( n T). mklist(n;f) T List |
|
primrec | Def primrec(n;b;c) == if n= 0 b else c(n-1,primrec(n-1;b;c)) fi (recursive) |
| | Thm* T:Type, n: , b:T, c:( n T T). primrec(n;b;c) T |
|
eq_int | Def i= j == if i=j true ; false fi |
| | Thm* i,j: . (i= j)  |
|
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)  |
|
le | Def A B == B<A |
| | Thm* i,j: . (i j) Prop |
|
append | Def as @ bs == Case of as; nil bs ; a.as' [a / (as' @ bs)] (recursive) |
| | Thm* T:Type, as,bs:T List. (as @ bs) T List |
|
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 |