let φ := hom.fn
α : Type u_1
β : Type u_2
G : group α
H : group β
hom : group_homomorphism G H
⊢ set_eq (kernel G H hom) (trivial_subgroup G) ↔ injective (group_homomorphism.fn G H)
α : Type u_1
β : Type u_2
G : group α
H : group β
hom : group_homomorphism G H
φ : α → β := group_homomorphism.fn G H
⊢ set_eq (kernel G H hom) (trivial_subgroup G) ↔ injective (group_homomorphism.fn G H)