subst c2
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 : 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))
V : VarAssignment D
h2_right : ¬isBoundIn v phi
h1 : v ≠ u → ¬isFreeIn v phi
h2_left : v ≠ u
x : VarName
a1_left : ¬x = u
a1_right : isFreeIn x phi
c2 : x = v
⊢ V x = a
D : Type
I : Interpretation D
u : VarName
a : D
head✝ : Definition
tail✝ : List Definition
phi : Formula
V : VarAssignment D
x : VarName
a1_left : ¬x = u
a1_right : isFreeIn x phi
tail_ih✝ :
  ∀ (V : VarAssignment D) (F : Formula),
    ¬isFreeIn x F →
      ¬isBoundIn x F →
        (Holds D I (Function.updateITE V u a) tail✝ F ↔
          Holds D I (Function.updateITE V x a) tail✝ (Sub.Var.One.Rec.fastReplaceFree u x F))
phi_ih :
  ∀ (V : VarAssignment D),
    ¬isFreeIn x phi →
      ¬isBoundIn x phi →
        (Holds D I (Function.updateITE V u a) (head✝ :: tail✝) phi ↔
          Holds D I (Function.updateITE V x a) (head✝ :: tail✝) (Sub.Var.One.Rec.fastReplaceFree u x phi))
h2_right : ¬isBoundIn x phi
h1 : x ≠ u → ¬isFreeIn x phi
h2_left : x ≠ u
⊢ V x = a