
theorem ReplaceValue:
  for f be real-valued FinSequence,
      i,j,k be Nat,
      a, b being Real st
    i in dom f & j in dom f & k in dom f & i <> j & (k <> i & k <> j) holds
    (Replace (f,i,j,a,b)).k = f.k
  proof
    let f be real-valued FinSequence,
        i,j,k be Nat,
        a,b be Real;
    assume
A1: i in dom f & j in dom f & k in dom f & i <> j & (k <> i & k <> j);
    (Replace (f,i,j,a,b)).k = (f +* (i,a)).k by A1,FUNCT_7:32
        .= f.k by A1,FUNCT_7:32;
    hence thesis;
  end;
