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;
reserve n       for Nat,
        a,b,c,d for Element of REAL n;

theorem Th50:
  n|-> r is Element of REAL n
  proof
A1: r is Element of REAL by XREAL_0:def 1;
    set f = n|-> r;
    reconsider f as Function;
    f in Funcs(Seg n,REAL)
    proof
      f is Element of n-tuples_on REAL by A1,FINSEQ_2:112;
      then f in n-tuples_on REAL;
      hence thesis by FINSEQ_2:93;
    end;
    hence thesis by FINSEQ_2:93;
  end;
