theorem :: ANPROJ10:50

for X being non empty set
for x being Tuple of 4,X
for P, Q, R, S being Element of X st x = <*P,Q,R,S*> holds
( pi_1234 x = <*P,Q,R,S*> & pi_1243 x = <*P,Q,S,R*> & pi_1324 x = <*P,R,Q,S*> & pi_1342 x = <*P,R,S,Q*> & pi_1423 x = <*P,S,Q,R*> & pi_1432 x = <*P,S,R,Q*> & pi_2134 x = <*Q,P,R,S*> & pi_2143 x = <*Q,P,S,R*> & pi_2314 x = <*Q,R,P,S*> & pi_2341 x = <*Q,R,S,P*> & pi_2413 x = <*Q,S,P,R*> & pi_2431 x = <*Q,S,R,P*> & pi_3124 x = <*R,P,Q,S*> & pi_3142 x = <*R,P,S,Q*> & pi_3214 x = <*R,Q,P,S*> & pi_3241 x = <*R,Q,S,P*> & pi_3412 x = <*R,S,P,Q*> & pi_3421 x = <*R,S,Q,P*> & pi_4123 x = <*S,P,Q,R*> & pi_4132 x = <*S,P,R,Q*> & pi_4213 x = <*S,Q,P,R*> & pi_4231 x = <*S,Q,R,P*> & pi_4312 x = <*S,R,P,Q*> & pi_4321 x = <*S,R,Q,P*> ) ;