reserve f for Function;
reserve n,k,n1 for Nat;
reserve r,p for Real;
reserve x,y,z for object;
reserve seq,seq1,seq2,seq3,seq9,seq19 for Real_Sequence;

theorem
  -seq1/"seq=(-seq1)/"seq & seq1/"(-seq)=-seq1/"seq
proof
  thus -seq1/"seq=(-1)(#)(seq1(#)(seq")) .=(-seq1)/"seq by Th18;
  thus seq1/"(-seq)=seq1(#)((-1)(#)seq") by Lm1,Th44
    .=-(seq1/"seq) by Th19;
end;
