Rank | Theorem | Name |
3 | Thm* k: , p:( k  k). Bij( k; k; p)  ( L: (k-1) List. p = compose_flips(L)) | [permute_by_flips] |
cites the following: |
0 | Thm* k: , i,j: k. Bij( k; k; (i, j)) | [flip_bijection] |
0 | Thm* f,g:(T T). Bij(T; T; f)  Bij(T; T; g)  Bij(T; T; f o g) | [compose_bij] |
0 | Thm* k: , f:( k  k).
Thm* 0<k
Thm* 
Thm* Bij( k; k; f)
Thm* 
Thm* f(k-1) = k-1  f (k-1)  (k-1) & Bij( (k-1); (k-1); f) | [bijection_restriction] |
2 | Thm* k: , x,y: k. L: (k-1) List. (x, y) = compose_flips(L) | [flip_adjacent] |
0 | Thm* k: , x,y: k. (y, x) o (y, x) = ( x.x) | [flip_inverse] |