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