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 Th47:
  for R being real-membered set for f being Function of T,R, t being Point of T
  st x in Seg n holds incl(f,n).t.x = f.t
  proof
    let R be real-membered set;
    let f be Function of T,R;
    let t be Point of T;
    assume
A1: x in Seg n;
    thus incl(f,n).t.x = (n |-> f.t).x by Def4
    .= f.t by A1,FINSEQ_2:57;
  end;
