theorem Th13:
  w1 = v & w2 = u implies w1 + w2 = v + u
proof
  assume
A1: v = w1 & u = w2;
  w1 + w2 = ((the addF of V)||the carrier of W).[w1,w2] by Def2;
  hence thesis by A1,FUNCT_1:49;
end;
