reserve x,y for object,X,Y,A,B,C,M for set;
reserve P,Q,R,R1,R2 for Relation;

theorem :: (27.2)
  (P /\ Q)*R c= (P*R) /\ (Q*R)
proof
  let x,y be object;
  assume [x,y] in (P /\ Q)*R;
  then consider z being object such that
A1: [x,z] in P/\Q and
A2: [z,y] in R by RELAT_1:def 8;
A3: [x,z] in P by A1,XBOOLE_0:def 4;
A4: [x,z] in Q by A1,XBOOLE_0:def 4;
A5: [x,y] in P*R by A2,A3,RELAT_1:def 8;
  [x,y] in Q*R by A2,A4,RELAT_1:def 8;
  hence thesis by A5,XBOOLE_0:def 4;
end;
