∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β]
  [inst_2 : PseudoEMetricSpace γ] {g : β →ᵈ γ} {f₁ f₂ : α →ᵈ β},
  Function.Injective ⇑g → (g.comp f₁ = g.comp f₂ ↔ f₁ = f₂)