interpretation "Subgroup image" 'subgroupimage H x =
(cic:/matita/algebra/groups/image.con _ _
- (cic:/matita/algebra/groups/morphism_of_subgroup.con _ H) x).
+ (cic:/matita/algebra/groups/morphism_OF_subgroup.con _ H) x).
definition member_of_subgroup ≝
λG.λH:subgroup G.λx:G.∃y.x=y \sub H.
(*CSC: here the coercion Type_of_Group cannot be omitted. Why? *)
theorem in_x_mk_left_coset_x_H:
- ∀G.∀x:Type_of_Group G.∀H:subgroup G.x ∈ (x*H).
+ ∀G.∀x:Type_OF_Group G.∀H:subgroup G.x ∈ (x*H).
intros;
simplify;
apply (ex_intro ? ? 1);