Denition 8.      *) satises the broken-angle property under a binary QCSP P* 
           ) must satisfy the property in Denition 8. 

            that is quantied arc consistent, P *is satisable if there exists a*
  
    
       *satises the QBTP*
 *For each existentially quantied variable x*     **                 
       *satises the QBAP under P*             
   is quantied arc consistent and      is quantied arc consistent according to Lemma
  satises the QBTP, so  is directional quantied globally consistent, and we can co     
           such that for each existentially quantied variable      

                    
                     
    ) such that for each existentially quantied variable         

         1 by a universally quantied variable can be achieved by the o   
         1 with an existentially quantied variable (we denote the va    
            
 

             
        


        
          
                              
                     
        
                             
                                 
    
              is quantied arc consistent,            
  
                        
     
                 
 
   
  
                satises the QBTP,       
           
                satises the QBTP and assignments to the variable in  
       
                ) satises the QBAP under    
                 
                          
                          
            

        
)-compatible for each existentially quantied variable       
        is satisable. 

                         
                               
                             
             satises the QBTP and the triple of variables () satises
                       
           *, there exists a polynomial-time algorithm to nd a mapping* 
                    