apply rule_C (P.and_ Q) ((exists_ v P).and_ (exists_ v Q)) v
case h1
P Q : Formula
v : VarName
⊢ IsDeduct {exists_ v (P.and_ Q)} ((exists_ v P).and_ (exists_ v Q))
case h1.h1
P Q : Formula
v : VarName
⊢ IsDeduct {exists_ v (P.and_ Q)} (exists_ v (P.and_ Q))

case h1.h2
P Q : Formula
v : VarName
⊢ IsDeduct ({exists_ v (P.and_ Q)} ∪ {P.and_ Q}) ((exists_ v P).and_ (exists_ v Q))

case h1.h3
P Q : Formula
v : VarName
⊢ ∀ H ∈ {exists_ v (P.and_ Q)}, ¬isFreeIn v H

case h1.h4
P Q : Formula
v : VarName
⊢ ¬isFreeIn v ((exists_ v P).and_ (exists_ v Q))