reserve A,B,C for non empty set,
  f for Function of [:A,B:],C;
reserve K for non empty doubleLoopStr;
reserve V for non empty ModuleStr over K;
reserve W for non empty RightModStr over K;

theorem
  for o being Function of [:the carrier of W, the carrier of K:], the
carrier of W, x being Scalar of K, y being Scalar of opp(K), v being Vector of
W, w being Vector of opp(W) st x=y & v=w holds (opp(o)).(y,w) = o.(v,x)
by FUNCT_4:def 8;
