rw [injective]
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
hphi : φ = group_homomorphism.fn G H
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
hphi : φ = group_homomorphism.fn G H
h : set_eq (kernel G H hom) (trivial_subgroup G)
⊢ ∀ (x y : α), group_homomorphism.fn G H x = group_homomorphism.fn G H y → x = y