case _ c1 =>
  rfl
D : Type
I : Interpretation D
V' : VarAssignment D
v t : VarName
head✝ : Definition
tail✝ : List Definition
tail_ih✝ :
  ∀ (V : VarAssignment D) (binders : Finset VarName) (F : Formula),
    fastAdmitsAux v t binders F →
      (∀ v ∉ binders, V' v = V v) →
        (Holds D I (Function.updateITE V v (V' t)) tail✝ F ↔ Holds D I V tail✝ (fastReplaceFree v t F))
x y : VarName
V : VarAssignment D
binders : Finset VarName
h1 : v = x ∨ v = y → t ∉ binders
h2 : ∀ v ∉ binders, V' v = V v
c1 : ¬v = y
⊢ V y = V y
no goals