reserve u,v,x,x1,x2,y,y1,y2,z,p,a for object,
        A,B,X,X1,X2,X3,X4,Y,Y1,Y2,Z,N,M for set;
reserve e for object, X,X1,X2,Y1,Y2 for set;

theorem
  for A,B being set st for x,y being set st x in A & y in B holds x
  misses y holds union A misses union B
proof
  let A,B be set such that
A1: for x,y being set st x in A & y in B holds x misses y;
  for y being set st y in B holds union A misses y
  proof
    let y be set;
    assume y in B;
    then for x being set st x in A holds x misses y by A1;
    hence thesis by Th79;
  end;
  hence thesis by Th79;
end;
