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

theorem Th38:
  for H being SubLoop of Q holds
  for x,y holds
  for x1,y1 being Element of H st
  x = x1 & y = y1
  holds
  x \ y = x1 \ y1
proof
  let H be SubLoop of Q;
  let x,y;
  let x1,y1 be Element of H;
  assume A1: x = x1 & y = y1;
   the carrier of H c= the carrier of Q by Def30;
  then reconsider x1y1 = x1 \ y1 as Element of Q;
  x * x1y1 = x1 * (x1 \ y1) by Th36,A1
  .= y by A1;
  hence thesis;
end;
