Rank | Theorem | Name |
5 | Thm* L:T List, i:(||L||-1), a,b:T.
Thm* a before b swap(L;i;i+1) a before b L a = L[(i+1)] & b = L[i] | [l_before_swap] |
cites the following: |
0 | Thm* L:T List, i,j:||L||. i<j [L[i]; L[j]] L | [sublist_pair] |
0 | Thm* k:, i,j:k. (i, j) kk | [flip_wf] |
4 | Thm* L:T List, i,j,x:||L||. swap(L;i;j)[x] = L[((i, j)(x))] | [swap_select] |
3 | Thm* L:T List, i,j:||L||. ||swap(L;i;j)|| = ||L|| | [swap_length] |
0 | Thm* k:, f:(k). increasing(f;k) (x,y:k. x<y f(x)<f(y)) | [increasing_implies] |