theorem Th41:
  seq is convergent implies lim(-seq)=-(lim seq)
proof
  assume seq is convergent;
  then lim ((-1)*seq)=(-1)*(lim seq) by Th39
    .=-(1*(lim seq)) by RLVECT_1:79
    .=-(lim seq) by RLVECT_1:def 8;
  hence thesis by Th11;
end;
