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:(kAProp).
Thm* (x:k. y:A. Q(x;y)) (f:(kA). 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 = ac) | [divides_def_on_nat] |
3 | Thm* x,y:. xy | [mul_nat_plus] |
4 | Thm* x:A, f:(AA), i,j,k:. k = ij f{i}{j}(x) = f{k}(x) A | [compose_iter_prod] |
1 | Thm* f:(AA), u:A. f(u) = u (i:. f{i}(u) = u) | [compose_iter_point_id] |