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

theorem Th7:
  x in X or x in Y implies x in X (\/) Y
proof
  assume
A1: x in X or x in Y;
  let i be object;
  assume
A2: i in I;
  then x.i in X.i or x.i in Y.i by A1;
  then x.i in X.i \/ Y.i by XBOOLE_0:def 3;
  hence thesis by A2,Def4;
end;
