reserve i,j,e,u for object;
reserve I for set; 
reserve x,X,Y,Z,V for ManySortedSet of I;

theorem Th17:
  Z c= X & Z c= Y implies Z c= X (/\) Y
proof
  assume
A1: Z c= X & Z c= Y;
  let i be object;
  assume
A2: i in I;
  then Z.i c= X.i & Z.i c= Y.i by A1;
  then Z.i c= X.i /\ Y.i by XBOOLE_1:19;
  hence thesis by A2,Def5;
end;
