sorry
case exists_
U V P_U P_V : Formula
l : List VarName
x✝ : VarName
P_u✝ P_v✝ : Formula
a✝ : IsReplOfFormulaInFormula U V P_u✝ P_v✝
a_ih✝ :
  (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v P_u✝ → v ∈ l) →
    IsProof ((Forall_ l (U.iff_ V)).imp_ (P_u✝.iff_ P_v✝))
h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v (exists_ x✝ P_u✝) → v ∈ l
⊢ IsProof ((Forall_ l (U.iff_ V)).imp_ ((exists_ x✝ P_u✝).iff_ (exists_ x✝ P_v✝)))
no goals