Rank | Theorem | Name |
6 | Thm* k: , f:( k inj k). i: . u: k. f{ i}(u) = u | [iter_perm_cycles_uniform] |
cites the following: |
4 | Thm* k: , f:( k inj k), u: k. i: . f{ i}(u) = u | [compose_iter_inj_cycles] |
0 | Thm* k: , Q:( k A Prop).
Thm* ( x: k. y:A. Q(x;y))  ( f:( k A). x: k. Q(x;f(x))) | [finite_choice] |
5 | Thm* a,b: , e:({a..b }  ), i:{a..b }. e(i) | ( i:{a..b }. e(i)) | [components_divide_iter_mul] |
2 | Thm* a,b: . a | b  ( c: . b = a c) | [divides_def_on_nat] |
3 | Thm* x,y: . x y   | [mul_nat_plus] |
4 | Thm* x:A, f:(A A), i,j,k: . k = i j  f{ i}{ j}(x) = f{ k}(x) A | [compose_iter_prod] |
1 | Thm* f:(A A), u:A. f(u) = u  ( i: . f{ i}(u) = u) | [compose_iter_point_id] |