Theorem: LO.FirstOrder.Rew.hom_id_eq (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
⊢ Rew.id.hom = LogicalConnective.Hom.id
Tactic:
ext p
State after:
case h
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
p : Semiformula L ξ n
⊢ Rew.id.hom p = LogicalConnective.Hom.id p

State before:
case h
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
p : Semiformula L ξ n
⊢ Rew.id.hom p = LogicalConnective.Hom.id p
Tactic:
induction p using Semiformula.rec' <;> simp[Rew.rel, Rew.nrel, *]
State after:
no goals