reserve X for non empty UNITSTR;
reserve a, b for Real;
reserve x, y for Point of X;
reserve X for RealUnitarySpace;
reserve x, y, z, u, v for Point of X;
reserve seq, seq1, seq2, seq3 for sequence of X;
reserve  n for Nat;

theorem Th44:
  for X being non empty addLoopStr, seq being sequence of X holds
  (-seq).n = - seq.n
  proof
    let X be non empty addLoopStr, seq be sequence of X;
A1: dom -seq = NAT by FUNCT_2:def 1;
A2: dom seq = NAT by FUNCT_2:def 1;
A3:  n in NAT by ORDINAL1:def 12;
    hence (-seq).n = (-seq)/.n by PARTFUN1:def 6,A1
    .= -seq/.n by A1,VFUNCT_1:def 5,A3
    .= - seq.n by A3,PARTFUN1:def 6,A2;
  end;
