reserve n,n1,n2,m for Nat;
reserve r,g1,g2,g,g9 for Complex;
reserve R,R2 for Real;
reserve s,s9,s1 for Complex_Sequence;

theorem
 for s being convergent Complex_Sequence
  holds lim (-s)*' = -(lim s)*'
proof
  let s being convergent Complex_Sequence;
  thus lim (-s)*' = (lim (-s))*' by Th11
    .= (-(lim s))*' by Th16
    .= -(lim s)*' by COMPLEX1:33;
end;

registration
  let s1,s2 be convergent Complex_Sequence;
  cluster s1 - s2 -> convergent for Complex_Sequence;
  coherence
proof
  - s2 is convergent;
  hence thesis;
end;
