Theorem: LO.FirstOrder.Rew.emb.hom_injective (Logic/FirstOrder/Basic/Syntax/Rew.lean)

State before:
L : Language
L₁ : Language
L₂ : Language
L₃ : Language
ξ : Type u_1
ξ₁ : Type u_2
ξ₂ : Type u_3
ξ₃ : Type u_4
n n₁ n₂✝ n₂ m m₁ m₂ m₃ : ℕ
o : Type u_5
e : IsEmpty o
⊢ Function.Injective ⇑emb.hom
Tactic:
simp[emb]
State after:
L : Language
L₁ : Language
L₂ : Language
L₃ : Language
ξ : Type u_1
ξ₁ : Type u_2
ξ₂ : Type u_3
ξ₃ : Type u_4
n n₁ n₂✝ n₂ m m₁ m₂ m₃ : ℕ
o : Type u_5
e : IsEmpty o
⊢ Function.Injective ⇑(map id fun a => e.elim a).hom

State before:
L : Language
L₁ : Language
L₂ : Language
L₃ : Language
ξ : Type u_1
ξ₁ : Type u_2
ξ₂ : Type u_3
ξ₃ : Type u_4
n n₁ n₂✝ n₂ m m₁ m₂ m₃ : ℕ
o : Type u_5
e : IsEmpty o
⊢ Function.Injective ⇑(map id fun a => e.elim a).hom
Tactic:
exact mapl_inj Function.injective_id (fun x => IsEmpty.elim e x)
State after:
no goals