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 Th10:
  the lmult of opp(W) = opp(the rmult of W)
proof
  reconsider p = ~(the rmult of W) as Function of [:the carrier of opp(K), the
  carrier of W:], the carrier of W;
  opp(W) = ModuleStr (# the carrier of W, the addF of W, 0.W, p #) by Def4;
  hence thesis;
end;
