push_neg at h2
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))
phi psi : Formula
phi_ih :
  ∀ (V : VarAssignment D),
    ¬isFreeIn v phi →
      ¬isBoundIn v phi →
        (Holds D I (Function.updateITE V u a) (head✝ :: tail✝) phi ↔
          Holds D I (Function.updateITE V v a) (head✝ :: tail✝) (Sub.Var.One.Rec.fastReplaceFree u v phi))
psi_ih :
  ∀ (V : VarAssignment D),
    ¬isFreeIn v psi →
      ¬isBoundIn v psi →
        (Holds D I (Function.updateITE V u a) (head✝ :: tail✝) psi ↔
          Holds D I (Function.updateITE V v a) (head✝ :: tail✝) (Sub.Var.One.Rec.fastReplaceFree u v psi))
V : VarAssignment D
h2 : ¬(isBoundIn v phi ∨ isBoundIn v psi)
h1 : ¬isFreeIn v phi ∧ ¬isFreeIn v psi
⊢ Holds D I (Function.updateITE V u a) (head✝ :: tail✝) (phi.iff_ psi) ↔
    Holds D I (Function.updateITE V v a) (head✝ :: tail✝) (Sub.Var.One.Rec.fastReplaceFree u v (phi.iff_ psi))
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))
phi psi : Formula
phi_ih :
  ∀ (V : VarAssignment D),
    ¬isFreeIn v phi →
      ¬isBoundIn v phi →
        (Holds D I (Function.updateITE V u a) (head✝ :: tail✝) phi ↔
          Holds D I (Function.updateITE V v a) (head✝ :: tail✝) (Sub.Var.One.Rec.fastReplaceFree u v phi))
psi_ih :
  ∀ (V : VarAssignment D),
    ¬isFreeIn v psi →
      ¬isBoundIn v psi →
        (Holds D I (Function.updateITE V u a) (head✝ :: tail✝) psi ↔
          Holds D I (Function.updateITE V v a) (head✝ :: tail✝) (Sub.Var.One.Rec.fastReplaceFree u v psi))
V : VarAssignment D
h1 : ¬isFreeIn v phi ∧ ¬isFreeIn v psi
h2 : ¬isBoundIn v phi ∧ ¬isBoundIn v psi
⊢ Holds D I (Function.updateITE V u a) (head✝ :: tail✝) (phi.iff_ psi) ↔
    Holds D I (Function.updateITE V v a) (head✝ :: tail✝) (Sub.Var.One.Rec.fastReplaceFree u v (phi.iff_ psi))