Rank | Theorem | Name |
5 | Thm* L:T List, x:T, i,j:{1..(||L||+1) }.
Thm* swap([x / L];i;j) = [x / swap(L;i-1;j-1)] | [swap_cons] |
cites the following: |
1 | Thm* a,b:T List. ||a|| = ||b||  ( i: . i<||a||  a[i] = b[i])  a = b | [list_extensionality] |
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* a:T, as:T List, i: . 0<i  i ||as||  [a / as][i] = as[(i-1)] | [select_cons_tl] |