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

theorem
  a_op(x,y,z) = 1.Q implies L_map(z,y,x) = z
proof
  assume a_op(x,y,z) = 1.Q;
  then L_map(z,y,x) = (x*y) \ ((x*y)*z) by Th9;
  hence thesis;
end;
