reserve n   for Nat,
        r,s for Real,
        x,y for Element of REAL n,
        p,q for Point of TOP-REAL n,
        e   for Point of Euclid n;
reserve n for non zero Nat;
reserve n for non zero Nat;
reserve n for Nat,
        X for set,
        S for Subset-Family of X;
reserve n for Nat,
        S for Subset-Family of REAL;

theorem Th41:
  Product(n,S) is Subset-Family of REAL n
  proof
    Product(n,S) is Subset-Family of product(Seg n --> REAL) by Th37;
    hence thesis by Th7;
  end;
