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

theorem Th36:
  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;
  x1 * y1 = ((the multF of Q)||the carrier of H).(x1,y1) by Def30
  .= x * y by A1,RING_3:1;
  hence thesis;
end;
