theorem Th72:
  [:P,Q:] c= Indices M & card P = card Q implies Det EqSegm(a*M,P,
  Q) = power(K).(a,card P) * Det EqSegm(M,P,Q)
proof
  assume that
A1: [:P,Q:] c= Indices M and
A2: card P = card Q;
  EqSegm(a*M,P,Q) = Segm(a*M,P,Q) by A2,Def3
    .= a * Segm(M,P,Q) by A1,Th63
    .= a * EqSegm(M,P,Q) by A2,Def3;
  hence thesis by Th71;
end;
