reserve N for Nat;
reserve n,m,n1,n2 for Nat;
reserve q,r,r1,r2 for Real;
reserve x,y for set;
reserve w,w1,w2,g,g1,g2 for Point of TOP-REAL N;
reserve seq,seq1,seq2,seq3,seq9 for Real_Sequence of N;

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;
