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

theorem Th115:
  X misses Y implies X (\) Y = X
proof
  assume
A1: X misses Y;
    let i be object;
    assume
A2: i in I;
    then
A3: (X (\) Y).i = X.i \ Y.i by Def6;
    X.i misses Y.i by A1,A2;
    hence (X (\) Y).i = X.i by A3,XBOOLE_1:83;
end;
