replace h : f₁.map g a = f₂.map g a := by simp [h]
case h
α : Sort u_1
β β✝ : Type u_2
g : β → β✝
f₁ f₂ : α ⇀ β
hi : Function.Injective g
h : map g f₁ = map g f₂
a : α
⊢ f₁ a = f₂ a
case h
α : Sort u_1
β β✝ : Type u_2
g : β → β✝
f₁ f₂ : α ⇀ β
hi : Function.Injective g
a : α
h : map g f₁ a = map g f₂ a
⊢ f₁ a = f₂ a