reserve f for Function;
reserve n,k,n1 for Element of NAT;
reserve r,p for Complex;
reserve x,y for set;
reserve seq,seq1,seq2,seq3,seq9,seq19 for Complex_Sequence;

theorem
  seq is non-zero implies -seq1/"seq=(-seq1)/"seq & seq1/"(-seq)=-seq1/" seq
proof
  assume
A1: seq is non-zero;
  thus -seq1/"seq=(-1r)(#)(seq1/"seq) .=((-1r)(#)seq1)(#)(seq") by Th12
    .=(-seq1)/"seq;
  thus seq1/"(-seq)=seq1(#)((-1r)(#)seq") by A1,Th40
    .=(-1r)(#)(seq1(#)(seq")) by Th13
    .=-(seq1/"seq);
end;
