simp only [def_and_]
case a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅
    (((P.imp_ (forall_ v Q)).imp_ (forall_ v (P.imp_ Q))).imp_
      (((forall_ v (P.imp_ Q)).imp_ (P.imp_ (forall_ v Q))).imp_
        (((forall_ v (P.imp_ Q)).imp_ (P.imp_ (forall_ v Q))).and_
          ((P.imp_ (forall_ v Q)).imp_ (forall_ v (P.imp_ Q))))))
case a.a
P Q : Formula
v : VarName
h1 : ¬isFreeIn v P
⊢ IsDeduct ∅
    (((P.imp_ (forall_ v Q)).imp_ (forall_ v (P.imp_ Q))).imp_
      (((forall_ v (P.imp_ Q)).imp_ (P.imp_ (forall_ v Q))).imp_
        (((forall_ v (P.imp_ Q)).imp_ (P.imp_ (forall_ v Q))).imp_
            ((P.imp_ (forall_ v Q)).imp_ (forall_ v (P.imp_ Q))).not_).not_))