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

State before:
L : Language
L' : Language
L₁ : Language
L₂ : Language
L₃ : Language
ξ : Type u_1
ξ' : Type u_2
ξ₁ : Type u_3
ξ₂ : Type u_4
ξ₃ : Type u_5
n n₁ n₂ n₃ : ℕ
ω : Rew L ξ₁ n₁ ξ₂ n₂
o : Type v₁
e : IsEmpty o
f : ξ₂ → Semiterm L ξ₃ n
⊢ (rewrite f).comp emb = emb
Tactic:
ext x <;> simp[comp_app]
State after:
case hf
L : Language
L' : Language
L₁ : Language
L₂ : Language
L₃ : Language
ξ : Type u_1
ξ' : Type u_2
ξ₁ : Type u_3
ξ₂ : Type u_4
ξ₃ : Type u_5
n n₁ n₂ n₃ : ℕ
ω : Rew L ξ₁ n₁ ξ₂ n₂
o : Type v₁
e : IsEmpty o
f : ξ₂ → Semiterm L ξ₃ n
x : o
⊢ (rewrite f) (emb &x) = emb &x

State before:
case hf
L : Language
L' : Language
L₁ : Language
L₂ : Language
L₃ : Language
ξ : Type u_1
ξ' : Type u_2
ξ₁ : Type u_3
ξ₂ : Type u_4
ξ₃ : Type u_5
n n₁ n₂ n₃ : ℕ
ω : Rew L ξ₁ n₁ ξ₂ n₂
o : Type v₁
e : IsEmpty o
f : ξ₂ → Semiterm L ξ₃ n
x : o
⊢ (rewrite f) (emb &x) = emb &x
Tactic:
{ exact IsEmpty.elim e x }
State after:
no goals

State before:
case hf
L : Language
L' : Language
L₁ : Language
L₂ : Language
L₃ : Language
ξ : Type u_1
ξ' : Type u_2
ξ₁ : Type u_3
ξ₂ : Type u_4
ξ₃ : Type u_5
n n₁ n₂ n₃ : ℕ
ω : Rew L ξ₁ n₁ ξ₂ n₂
o : Type v₁
e : IsEmpty o
f : ξ₂ → Semiterm L ξ₃ n
x : o
⊢ (rewrite f) (emb &x) = emb &x
Tactic:
exact IsEmpty.elim e x
State after:
no goals