apply bind_eq_bind_of_eq
L : Language
μ : Type v
α : Type u_1
inst✝³ : Primcodable α
inst✝² : Primcodable μ
inst✝¹ : (k : ℕ) → Primcodable (L.Func k)
inst✝ : UniformlyPrimcodable L.Func
k : ℕ
t : Semiterm L μ k
⊢ UTerm.bind (fun x => if x < k then UTerm.bvar (x + 1) else default) (fun x => UTerm.fvar x) ↑(subtEquiv t) =
    UTerm.bind (fun x => UTerm.bvar (x + 1)) UTerm.fvar ↑(subtEquiv t)
case hb
L : Language
μ : Type v
α : Type u_1
inst✝³ : Primcodable α
inst✝² : Primcodable μ
inst✝¹ : (k : ℕ) → Primcodable (L.Func k)
inst✝ : UniformlyPrimcodable L.Func
k : ℕ
t : Semiterm L μ k
⊢ ∀ x < (↑(subtEquiv t)).bv, (if x < k then UTerm.bvar (x + 1) else default) = UTerm.bvar (x + 1)

case he
L : Language
μ : Type v
α : Type u_1
inst✝³ : Primcodable α
inst✝² : Primcodable μ
inst✝¹ : (k : ℕ) → Primcodable (L.Func k)
inst✝ : UniformlyPrimcodable L.Func
k : ℕ
t : Semiterm L μ k
⊢ ∀ (x : μ), UTerm.fvar x = UTerm.fvar x