split_ifs <;> tauto
case a.h.e'_2
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 y : VarName
V : VarAssignment D
h1 : ¬(v = x ∨ v = y)
h2 : ¬isBoundIn v (eq_ x y)
⊢ (if x = u then a else V x) = if (if u = x then v else x) = v then a else V (if u = x then v else x)
no goals