rfl
D : Type
I : Interpretation D
u v : VarName
a : D
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
  ∀ (V : VarAssignment D) (F : Formula),
    ¬isFreeIn v F →
      ¬isBoundIn v F →
        (Holds D I (Function.updateITE V u a) tail✝ F ↔
          Holds D I (Function.updateITE V v a) tail✝ (Sub.Var.One.Rec.fastReplaceFree u v F))
X : PredName
xs : List VarName
V : VarAssignment D
h1 : v ∉ xs
h2 : ¬isBoundIn v (pred_var_ X xs)
x : VarName
a1 : x ∈ xs
c1 : u = x
c2 : v = v
⊢ a = a
no goals