reserve
  x for object, X for set,
  i, n, m for Nat,
  r, s for Real,
  c, c1, c2, d for Complex,
  f, g for complex-valued Function,
  g1 for n-element complex-valued FinSequence,
  f1 for n-element real-valued FinSequence,
  T for non empty TopSpace,
  p for Element of TOP-REAL n;

theorem
  n in Seg m implies PROJ(m,n) is continuous
  proof
    assume
A1: n in Seg m;
A2: m in NAT by ORDINAL1:def 12;
    for p being Element of TOP-REAL m holds PROJ(m,n).p = p/.n by Def6;
    hence thesis by A2,A1,JORDAN2B:18;
  end;
