SC
case a.a
U V P_U P_V : Formula
l : List VarName
h1_P h1_Q h1_P' h1_Q' : Formula
h1_1 : IsReplOfFormulaInFormula U V h1_P h1_P'
h1_2 : IsReplOfFormulaInFormula U V h1_Q h1_Q'
h1_ih_1 :
  (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_P → v ∈ l) →
    IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_P.iff_ h1_P'))
h1_ih_2 :
  (∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ isBoundIn v h1_Q → v ∈ l) →
    IsProof ((Forall_ l (U.iff_ V)).imp_ (h1_Q.iff_ h1_Q'))
h2 : ∀ (v : VarName), (isFreeIn v U ∨ isFreeIn v V) ∧ (isBoundIn v h1_P ∨ isBoundIn v h1_Q) → v ∈ l
⊢ IsDeduct ∅
    (((Forall_ l ((U.imp_ V).imp_ (V.imp_ U).not_).not_).imp_ ((h1_Q.imp_ h1_Q').imp_ (h1_Q'.imp_ h1_Q).not_).not_).imp_
      (((Forall_ l ((U.imp_ V).imp_ (V.imp_ U).not_).not_).imp_
            ((h1_P.imp_ h1_P').imp_ (h1_P'.imp_ h1_P).not_).not_).imp_
        ((Forall_ l ((U.imp_ V).imp_ (V.imp_ U).not_).not_).imp_
          (((h1_P.imp_ h1_Q).imp_ (h1_P'.imp_ h1_Q')).imp_ ((h1_P'.imp_ h1_Q').imp_ (h1_P.imp_ h1_Q)).not_).not_)))
no goals