<k>
    .K
</k>
<mgu>
    subst(.KList)
</mgu>
<ctx-stack>
    .List
</ctx-stack>
<sig>
    Name ( "Person" ) |-> Set ( 0 )
    Name ( "implication" ) |-> ( #symVariable(17) : (Name ( "IsStudent" ) Name
       ( "mary" )) ) -> (Name ( "IsStudent" ) Name ( "john" ))
    Name ( "mary" ) |-> Name ( "Person" )
    Name ( "maryIsStudent" ) |-> (Name ( "IsStudent" ) Name ( "mary" ))
    Fun ( "Lemma1" ) |-> Set ( 0 )
    Fun ( "Lemma2" ) |-> Set ( 0 )
    Fun ( "proof-lemma1" ) |-> Fun ( "Lemma1" )
    Fun ( "proof-lemma2" ) |-> Fun ( "Lemma2" )
    Postlt ( "IsStudent" ) |-> ( #symVariable(4) : Name ( "Person" ) ) -> Set 
      ( 0 )
    Postlt ( "barbara" ) |-> Name ( "Person" )
    Postlt ( "john" ) |-> Name ( "Person" )
</sig>
<ctx>
    .Map
</ctx>
<meta>
    .Map
</meta>
<ncat>
    Name ( "IsStudent" ) |-> Postlt ( "IsStudent" )
    Name ( "Lemma1" ) |-> Fun ( "Lemma1" )
    Name ( "Lemma2" ) |-> Fun ( "Lemma2" )
    Name ( "barbara" ) |-> Postlt ( "barbara" )
    Name ( "john" ) |-> Postlt ( "john" )
    Name ( "proof-lemma1" ) |-> Fun ( "proof-lemma1" )
    Name ( "proof-lemma2" ) |-> Fun ( "proof-lemma2" )
</ncat>
<fun>
    Fun ( "Lemma1" ) |-> (Name ( "IsStudent" ) Name ( "john" ))
    Fun ( "Lemma2" ) |-> ( #symVariable(3) : (Postlt ( "IsStudent" ) Postlt ( 
      "john" )) ) -> (Postlt ( "IsStudent" ) Name ( "barbara" ))
    Fun ( "proof-lemma1" ) |-> (Name ( "implication" ) Name ( "maryIsStudent" 
      ))
    Fun ( "proof-lemma2" ) |-> \ ( Var ( "x" ) : (Postlt ( "IsStudent" ) 
      Postlt ( "john" )) ) -> #symExpr(55)
</fun>
