intro D I V E _
Δ : List Formula
F : Formula
v t : VarName
phi : Formula
⊢ ∀ (D : Type) (I : Interpretation D) (V : VarAssignment D) (E : Env),
    (∀ H ∈ [], Holds D I V E H) →
      Holds D I V E ((forall_ v phi).imp_ (Sub.Var.All.Rec.Fresh.sub (Function.updateITE id v t) freshChar phi))
Δ : List Formula
F : Formula
v t : VarName
phi : Formula
D : Type
I : Interpretation D
V : VarAssignment D
E : Env
a✝ : ∀ H ∈ [], Holds D I V E H
⊢ Holds D I V E ((forall_ v phi).imp_ (Sub.Var.All.Rec.Fresh.sub (Function.updateITE id v t) freshChar phi))