Theorem: LO.FirstOrder.Rew.substs_comp_embSubsts (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
k : ℕ
w✝ : Fin k → Semiterm L ξ n
l : ℕ
v : Fin l → Semiterm L ξ k
w : Fin k → Semiterm L ξ n
⊢ (substs w).comp (embSubsts v) = embSubsts (⇑(substs w) ∘ v)
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
k : ℕ
w✝ : Fin k → Semiterm L ξ n
l : ℕ
v : Fin l → Semiterm L ξ k
w : Fin k → Semiterm L ξ n
x : Empty
⊢ (substs w) ((embSubsts v) &x) = (embSubsts (⇑(substs w) ∘ v)) &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
k : ℕ
w✝ : Fin k → Semiterm L ξ n
l : ℕ
v : Fin l → Semiterm L ξ k
w : Fin k → Semiterm L ξ n
x : Empty
⊢ (substs w) ((embSubsts v) &x) = (embSubsts (⇑(substs w) ∘ v)) &x
Tactic:
exact Empty.elim x
State after:
no goals