Theorem: LO.FirstOrder.Rew.substs_comp_bShift_eq_id (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
v : Fin 1 → Semiterm L ξ 0
⊢ (substs v).comp bShift = Rew.id
Tactic:
ext x <;> simp[comp_app]
State after:
case hb
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
v : Fin 1 → Semiterm L ξ 0
x : Fin 0
⊢ v x.succ = #x

State before:
case hb
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
v : Fin 1 → Semiterm L ξ 0
x : Fin 0
⊢ v x.succ = #x
Tactic:
exact Fin.elim0 x
State after:
no goals