Theorem: LO.FirstOrder.Rew.free_comp_substs_eq_substs_comp_shift (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
Lf : Language
n' : ℕ
w : Fin n' → SyntacticSemiterm Lf (n + 1)
⊢ Rew.comp free (substs w) = (substs (⇑free ∘ w)).comp shift
Tactic:
ext x <;> simp[comp_app]
State after:
no goals