intro a2
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
s1 :
  Holds D I V E (Sub.Var.All.Rec.Fresh.sub (Function.updateITE id v t) freshChar phi) ↔
    Holds D I (V ∘ Function.updateITE id v t) E phi
⊢ (∀ (d : D), Holds D I (Function.updateITE V v d) E phi) →
    Holds D I V E (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
s1 :
  Holds D I V E (Sub.Var.All.Rec.Fresh.sub (Function.updateITE id v t) freshChar phi) ↔
    Holds D I (V ∘ Function.updateITE id v t) E phi
a2 : ∀ (d : D), Holds D I (Function.updateITE V v d) E phi
⊢ Holds D I V E (Sub.Var.All.Rec.Fresh.sub (Function.updateITE id v t) freshChar phi)