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);
theorem foo:
∀G.∀H:normal_subgroup G.∀x.x*H=H*x.
*)
-
+(*
theorem member_of_left_coset_mk_left_coset_x_H_a_to_member_of_left_coset_mk_left_coset_y_H_b_to_member_of_left_coset_mk_left_coset_op_x_y_H_op_a_b:
∀G.∀H:normal_subgroup G.∀x,y,a,b.
a ∈ (x*H) → b ∈ (y*H) → (a·b) ∈ ((x·y)*H).
intros;
simplify;
-qed.
\ No newline at end of file
+qed.
+*)