reserve Q,Q1,Q2 for multLoop;
reserve x,y,z,w,u,v for Element of Q;

theorem Th39:
  for H being SubLoop of Q holds
  for x,y st x in the carrier of H & y in the carrier of H holds
    x \ y in the carrier of H
proof
  let H be SubLoop of Q, x,y such that
  A1: x in the carrier of H & y in the carrier of H;
  reconsider x1 = x,y1=y  as Element of H by A1;
  x \ y = x1 \ y1 by Th38;
  hence thesis;
end;
